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</h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1065/statistics-and-probability.html">Statistics and Probability</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">4.5 & 4.6 Probability</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <h2><img alt="" src="../../files/LSP/PB/PB-small-1.jpeg" style="width: 100px; height: 100px; float: left;">What are the chances?</h2> <div>This unit is all about probability - the study of chance. For many students, much of this is revision of previous experiences with some new ideas thrown in. The unit covers the fundamental ideas, language notation, combined events and conditional probability. You will be expected to work with sample space, tree and Venn diagrams as well as reading from tables. This page has everything you need to learn, understand and practice working with these ideas. <hr> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><meta charset="utf-8"></p> <p dir="ltr"><b id="docs-internal-guid-0f50c3a3-7fff-b164-51f2-8c068a5bc7d9">In this unit you should learn to…</b></p> <ul> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">recognise key terms</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">calculate using sample space diagrams</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">use tree diagrams</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">find probabilities from tables and Venn diagrams</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">use conditional probability</p> </li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Slides Gallery - Probability Part 1</p> </div> </div> <div class="panel-body"> <div> <div>This first section covers the ideas, language, notation as well as combined events with sample space and tree diagrams. Use these slides to review the material and key points covered in the videos.</div> <div> <div id="carousel-247" class="dynamic-gallery carousel slide" data-id="247"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos003.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos004.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos005.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos006.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos007.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos008.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos008.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos009.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos009.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos010.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos010.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos001.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-247/probability-show-1-no-logos002.jpeg" data-fancybox="gallery-247" title="" data-caption=""><img alt="" src="../../../std-galleries/15-247/probability-show-1-no-logos002.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-247" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-247" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos003-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos004-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos005-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos006-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos007-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos008-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos009-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos010-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos001-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-247/probability-show-1-no-logos002-thumb128.jpg"><li></li></ol> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. Ideas, language and notation - Part 1</p> </div> </div> <div class="panel-body"> <div> <p>This is an introduction to the key ideas and terms in this study of probability.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592627469"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Ideas, language and notation - Part 2</p> </div> </div> <div class="panel-body"> <div> <p>In this video we move on to more details about the idea, language and terminology.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592627883"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. Sample Space and Combined events</p> </div> </div> <div class="panel-body"> <div> <p>Sample space diagrams are a relatively straightforward way of looking outcomes for two combined events. Here we will look at one in the context of an example and how it can be used to deduce probabilities. We will cover the AND and OR rules for combined events here.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592629167"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. Tree Diagrams and Combined events</p> </div> </div> <div class="panel-body"> <div> <p>Here will look at how tree diagrams can achieve the same thing and go on to be more versatile than the sample space. We will cover the AND and OR rules for combined events here.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592629878"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>5. Tree Diagrams 'Without Replacement'</p> </div> </div> <div class="panel-body"> <div> <p>The idea of 'Without replacement' is a really important one. This is when the probabilities of a second event depend on the outcome of the previous event.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592630298"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Slides - Probability part 2</p> </div> </div> <div class="panel-body"> <div> <p>This section covers the following - Probability from tables and Venn diagrams, Conditional probability and the laws of Probability. Use these slides to review the material and key points covered in the videos.</p> <div id="carousel-248" class="dynamic-gallery carousel slide" data-id="248"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos002.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos003.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos004.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos005.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos006.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos007.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos008.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos008.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos009.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos009.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos010.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos010.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-248/probability-2-nologos001.jpeg" data-fancybox="gallery-248" title="" data-caption=""><img alt="" src="../../../std-galleries/15-248/probability-2-nologos001.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-248" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-248" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos002-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos003-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos004-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos005-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos006-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos007-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos008-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos009-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos010-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-248/probability-2-nologos001-thumb128.jpg"><li></li></ol> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>6. Probabilities from Tables</p> </div> </div> <div class="panel-body"> <p>Often we can deduce probabilities from a simple table of results. Here we will look at such an example which will lead nicely into the later section on Conditional Probability.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/701251120"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>7. Probabilities from Venn Diagrams</p> </div> </div> <div class="panel-body"> <div> <p>This section focusses on linking set theory, Venn diagrams and probability together. How we deduce probabilities from Venn diagrams?</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592631317"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>8. Conditional Probability</p> </div> </div> <div class="panel-body"> <p>This is a key concept to get your heads around. This section has three videos that go through conditional probability in the context of a) A table of results, b) A tree diagram and c) a Venn diagram. This idea is probably most easily understood from the 'Table of results' context and can be quite intuitive.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592631987"></iframe></div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592632962"></iframe></div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592633249"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>9. The Laws of Probability</p> </div> </div> <div class="panel-body"> <div> <p>These are sophisticated concepts that summarise in general, much of what is already understood by this point. Have at go at following and understanding the laws for Combined events, mutually exclusive events, independent events and conditional probability.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592633793"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <p>This section of the page can be used for quick review. The flashcards help you go over key points and the quiz lets you practice answering questions on this subtopic.</p> <h4>Revision Cards</h4> <p>Review these condensed 'key point' revision cards to help you check and keep ideas fresh in your mind.</p> <div id="carousel-61" class="dynamic-gallery carousel slide" data-id="61"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/3-61/fc1.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc1.jpg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/3-61/fc2.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc2.jpg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/3-61/fc3.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc3.jpg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/3-61/fc4.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc4.jpg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/3-61/fc5.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc5.jpg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/3-61/fc6.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc6.jpg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/3-61/fc7.jpg" data-fancybox="gallery-61" title="" data-caption=""><img alt="" src="../../../std-galleries/3-61/fc7.jpg"></a></div></div><a class="left carousel-control" href="#carousel-61" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-61" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/3-61/fc1-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/3-61/fc2-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/3-61/fc3-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/3-61/fc4-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/3-61/fc5-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/3-61/fc6-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/3-61/fc7-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self Checking Quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-324-2258"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p><img alt="" src="../../files/LSP/PB/8dice.jpg" style="float: left; width: 50px; height: 51px;">Consider an 8 sided dice. The dice is unbiased and the sides are numbered from 1 to 8. Fill the gaps to give the respective probabilities. (Your answers are expected as exact decimals between 0 and 1, for example 0.65)</p></div><div class="q-answer"><p>What is the probability of getting......</p><ol><li>The number 3, <input type="text" style="height: auto;" data-c="0.125"> <span class="review"></span> </li><li>NOT the number 7, <input type="text" style="height: auto;" data-c="0.875"> <span class="review"></span> </li><li>A prime number, <input type="text" style="height: auto;" data-c="0.5"> <span class="review"></span> </li><li>A number less than 4, <input type="text" style="height: auto;" data-c="0.375"> <span class="review"></span> </li><li>A number NOT equal to 6 or less, <input type="text" style="height: auto;" data-c="0.25"> <span class="review"></span> </li><li>A number that is prime AND odd, <input type="text" style="height: auto;" data-c="0.375"> <span class="review"></span> </li><li>A number that is prime OR odd <input type="text" style="height: auto;" data-c="0.625"> <span class="review"></span> </li><li>A multiple of 9, <input type="text" style="height: auto;" data-c="0"> <span class="review"></span> </li></ol></div><div class="q-explanation"><p>The probability of any given number is 1/8 = 0.125 . All the answers are a various multiples of that probability</p><ol><li>3 - 1 out of 8</li><li>1, 2, 3, 4, 5, 6 and 7 - 7 out of 8</li><li>Primes are 2, 3, 5 and 7 - 4 out of 8 (careful not to include 1 and not toforget 2)</li><li>1, 2 and 3 - 3 out of 8 (4 is not less than 4)</li><li>7 and 8 - 2 out of 8</li><li>3, 5 and 7 - 3 out of 8 (see answer to part 4 to help)</li><li>1, 2, 3, 5 and 7 - 5 out of 8</li><li>None - 0 (There are no mulitples of 9 available)</li></ol></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>.....</p><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Match the correct description to the notation below (Enter a capital letter in the answer box)</p><p>A - <span class="math-tex">\(P(A')\)</span></p><p>B - <span class="math-tex">\(P(A\cup B)\)</span> </p><p>C - <span class="math-tex">\(P(A)\)</span></p><p>D - <span class="math-tex">\(P(A|B)\)</span></p><p>E - <span class="math-tex">\(P(A\cap B)\)</span></p></div><div class="q-answer"><p>The probability of event A happening <input type="text" style="height: auto;" data-c="C"> <span class="review"></span> </p><p>The probability of event A AND B happening <input type="text" style="height: auto;" data-c="E"> <span class="review"></span> </p><p>The probability of event A GIVEN event B <input type="text" style="height: auto;" data-c="D"> <span class="review"></span> </p><p>The probability of NOT event A <input type="text" style="height: auto;" data-c="A"> <span class="review"></span> </p><p>The probability of event A OR event B happening <input type="text" style="height: auto;" data-c="B"> <span class="review"></span> </p></div><div class="q-explanation"><p>You might need to revisit some of the work on set notation to help with this question.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>In a factory producing plastic toilet cleaning attachments (toilet ducks), it is observed that for every 500 items produced, 3 are defective.</p></div><div class="q-answer"><p>What is the probability of a random selected item being defective? Give your answer in standard index form, <span class="math-tex">\(a\quad \times \quad { 10 }^{ k }\quad \)</span> where a =<input type="text" style="height: auto;" data-c="6"> <span class="review"></span> and k = <input type="text" style="height: auto;" data-c="-3"> <span class="review"></span> </p><p>In a month, the factory produces 15600 such items. How many of these items are likely to be found as defective in that time. (Round your answer to the nearest whole number) <input type="text" style="height: auto;" data-c="94"> <span class="review"></span> </p></div><div class="q-explanation"><p>Part 1 - 3 divided by 500 = 0.006 which is 6 x 10<sup>-3</sup> in standard index form</p><p>Part 2 - 15600 x 0.006 = 93.6 which rounds to 94</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p><img alt="" src="../../files/LSP/PB/10d4s.jpg" style="float: left; width: 100px; height: 48px;">A 10 side dice is rolled (unbiased, numbered from 1 to 10) and a a four coloured spinner is spun (unbiased and equally divided between Red, Green, Blue and Orange)</p></div><div class="q-answer"><ol><li>What is the total number of possible outcomes? <input type="text" style="height: auto;" data-c="40"> <span class="review"></span> </li><li>What is the probability of getting an even number and green? (give answer as a decimal) <input type="text" style="height: auto;" data-c="0.125"> <span class="review"></span> </li><li>What is the probability of getting a number less than 8 AND Blue? <input type="text" style="height: auto;" data-c="0.175"> <span class="review"></span> </li><li>What is the probability of getting (Red OR Orange) AND a number bigger than 3? <input type="text" style="height: auto;" data-c="0.35"> <span class="review"></span></li></ol></div><div class="q-explanation"><p>A sample space diagram should help to answer this question.</p><p style="text-align: center;"><img alt="" src="../../files/LSP/PB/q4ss.jpg" style="width: 400px; height: 148px;"></p><ol><li>There are 4 possible colours for each of the 10 numbers of the dice</li><li>5 out of 40</li><li>7 out of 40</li><li>14 out of 40, 20 out of 40 are Green OR Red, of those, 14 are bigger than 3</li></ol></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>....</p><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>The probability of Ellie being late for school on any given day is 0.1</p><p>The probability of Manny being late for school on any given day is 0.12</p><p>The events are INDEPENDENT and can be represented by the tree diagram below</p><p style="text-align: center;"><img alt="" src="../../files/LSP/PB/q5.jpg" style="width: 400px; height: 319px;"></p></div><div class="q-answer"><p>1. What should the values of a, b and c be?</p><p>a = <input type="text" style="height: auto;" data-c="0.9"> <span class="review"></span> b = <input type="text" style="height: auto;" data-c="0.12"> <span class="review"></span> c = <input type="text" style="height: auto;" data-c="0.88"> <span class="review"></span> </p><p>2. What is the probability that both Ellie and Manny will be late? <input type="text" style="height: auto;" data-c="0.012"> <span class="review"></span> </p><p>3. What is the probability Ellie will be late but not Manny? <input type="text" style="height: auto;" data-c="0.088"> <span class="review"></span> </p><p>4. What is the probability that Exactly one of them will be late, but not the other? <input type="text" style="height: auto;" data-c="0.196"> <span class="review"></span> </p></div><div class="q-explanation"><ol><li>a = 1 - 0.1 = 0.9, b = 0.12 (given in the question), c = 1 - 0.12 = 0.88</li><li>0.1 x 0.12 = 0.012</li><li>0.1 x 0.88 = 0.088</li><li>From part 3, Ellie late but not Manny is 0.88. Ellie on time but Manny late = 0.9 x 0.12 = 0.108. Together we get 0.088 + 0.108 = 0.196</li></ol></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p><img alt="" src="../../files/LSP/PB/q6qs.jpg" style="float: left; width: 80px; height: 81px;">In a party bag of chocolates there are 3 purple and 7 red chocolates. You select 1 of them at random (Without looking) and eat it! Then you go back for a second one, also without looking. The following tree diagram shows the possible outcomes on a tree diagram.</p><p style="text-align: center;"><img alt="" src="../../files/LSP/PB/q6td.jpg" style="width: 400px; height: 359px;"></p></div><div class="q-answer"><p>1. What are the values of a, b, c, d and e, assuming that a/b is written in its simplest form.</p><p>a = <input type="text" style="height: auto;" data-c="2"> <span class="review"></span> , b = <input type="text" style="height: auto;" data-c="9"> <span class="review"></span> , c = <input type="text" style="height: auto;" data-c="7"> <span class="review"></span> ,</p><p>d = <input type="text" style="height: auto;" data-c="3"> <span class="review"></span> , e = <input type="text" style="height: auto;" data-c="6"> <span class="review"></span> </p><p>2. What is the probability that both chocolates will be red? (Give your answer as a decimal correct to 3sf) <input type="text" style="height: auto;" data-c="0.156"> <span class="review"></span> </p><p>3. What is the probability that there will be at least one red one? (Give your answer as a decimal correct to 3sf) <input type="text" style="height: auto;" data-c="0.933"> <span class="review"></span> </p><p>4. What is the probability that you wil have one of each colour? Give your answer as a decimal correct to 3sf) <input type="text" style="height: auto;" data-c="0.467"> <span class="review"></span> </p></div><div class="q-explanation"><p>1. a = 2, if the 1st was purple there are only 2 left, b = 9, there are only 9 left all together, c = 7 - there are still 7 red ones left, d = 3 - there are still 3 red ones left, e = 6 - the ifrst was red so there is only six red ones left.</p><p>2. <span class="math-tex">\(\frac { 7 }{ 10 } \times \frac { 2 }{ 9 } =\frac { 14 }{ 90 } =0.156\quad (3sf)\)</span></p><p>3. 1 subtract the probability they are both purple, <span class="math-tex">\(1\quad -\quad \frac { 3 }{ 10 } \times \frac { 2 }{ 9 } =\quad 0.933\quad (3sf)\)</span></p><p>4. <span class="math-tex">\(\frac { 3 }{ 10 } \times \frac { 7 }{ 9 } \quad +\quad \frac { 7 }{ 10 } \times \frac { 3 }{ 9 } \quad =\quad 0.467\quad (3sf)\)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>The probability of Diego leaving the house on time is 0.75. If he leaves on time then the probability of getting stuck in traffic on the way is 0.4. If he leaves late then the probability of getting stuck in traffic is 0.8. The information can be shown on the following tree diagram.</p><p style="text-align: center;"><img alt="" src="../../files/LSP/PB/q7td.jpg" style="width: 500px; height: 405px;"></p></div><div class="q-answer"><p>1. What are the exact values of a, b, c, d and e?</p><p>a = <input type="text" style="height: auto;" data-c="0.25"> <span class="review"></span> , b = <input type="text" style="height: auto;" data-c="0.4"> <span class="review"></span> , c = <input type="text" style="height: auto;" data-c="0.6"> <span class="review"></span> </p><p>d = <input type="text" style="height: auto;" data-c="0.8"> <span class="review"></span> , e = <input type="text" style="height: auto;" data-c="0.2"> <span class="review"></span> </p><p>2. What is the probability that Diego will be late but not get stuck in traffic? (exact answer) <input type="text" style="height: auto;" data-c="0.05"> <span class="review"></span> </p><p>3. What is the probability that Diego will get stuck in traffic? (exact answer) <input type="text" style="height: auto;" data-c="0.5"> <span class="review"></span> </p><p>4. What is the probablity that Diego left on time, given that he got stuck? (exact answer) <input type="text" style="height: auto;" data-c="0.6"> <span class="review"></span> </p></div><div class="q-explanation"><p>1. a = 1 - 0.75, b = 0.4, given, c = 1 - 0.4, d = 0.8, given, e = 1 - 0.8</p><p>2. 0.25 x 0.2 = 0.05</p><p>3. 0.75 x 0.4 + 0.25 x 0.8 = 0.5</p><p>4. <span class="math-tex">\(\frac { Probability\quad on\quad time\quad and\quad stuck }{ Probability\quad stuck } =\quad \frac { 0.75\times 0.4 }{ 0.5 } =\frac { 0.3 }{ 0.5 } =0.6\)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following table shows the results of a survey comparing gender with favourite film genre....</p><p style="text-align: center;"><img alt="" src="../../files/LSP/PB/q7table.jpg" style="width: 500px; height: 272px;"></p></div><div class="q-answer"><p>A person from the survey is selected at random. What is the probability that.... (Give your answers as demilas correct to 3sf)</p><p>1. Male <input type="text" style="height: auto;" data-c="0.442"> <span class="review"></span> </p><p>2. Prefers Drama <input type="text" style="height: auto;" data-c="0.372"> <span class="review"></span> </p><p>3. Is Male AND prefers Comedy <input type="text" style="height: auto;" data-c="0.102"> <span class="review"></span> </p><p>4. Is Female OR prefers Horror <input type="text" style="height: auto;" data-c="0.633"> <span class="review"></span> </p><p>5. Prefers Action AND is Female <input type="text" style="height: auto;" data-c="0.149"> <span class="review"></span> </p><p>6. Prefers Comedy OR is Male <input type="text" style="height: auto;" data-c="0.498"> <span class="review"></span> </p><p>7. Prefers Drama, given that they are male <input type="text" style="height: auto;" data-c="0.337"> <span class="review"></span> </p><p>8. Is Female, given that they prefer Action <input type="text" style="height: auto;" data-c="0.583"> <span class="review"></span> </p></div><div class="q-explanation"><p>All answers rounded to 3sf.</p><p>1. 95/215 = 0.442</p><p>2. 80/215 = 0.372</p><p>3. 22/215 = 0.102 (Only 22 people are both)</p><p>4. 136/215 = 0.633 (120 females + 16 males who like horror)</p><p>5. 35/215 = 0.149 (Only 35 people who are both)</p><p>6. 107/215 = 0.498 (34 people who prefer comedy + 25 + 32 + 16 males who prefer other genres)</p><p>7. 32/95 = 0.337 (Only considering the 95 males of which 32 prefer drama)</p><p>8. 35/60 = 0.583 (Only considering the 60 people who prefer action of which 35 are female)</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following Venn diagram shows the frequencies of elements of the sets A and B.</p><p style="text-align: center;"><img alt="" src="../../files/LSP/PB/q9vd.jpg" style="width: 500px; height: 290px;"></p></div><div class="q-answer"><p>What is the probability that an element selected at random will be in the following sets.... </p><p>(Give your answers as demilas correct to 3sf)</p><p>1. <span class="math-tex">\(P(A)\)</span> = <input type="text" style="height: auto;" data-c="0.585"> <span class="review"></span> </p><p>2. <span class="math-tex">\(P(A\cup B)\)</span> = <input type="text" style="height: auto;" data-c="0.811"> <span class="review"></span> </p><p>3. <span class="math-tex">\(P(A\cap B)\)</span> = <input type="text" style="height: auto;" data-c="0.113"> <span class="review"></span> </p><p>4.<span class="math-tex">\(P(A|B)\)</span> = <input type="text" style="height: auto;" data-c="0.333"> <span class="review"></span> </p><p>5. <span class="math-tex">\(P(B')\)</span> = <input type="text" style="height: auto;" data-c="0.660"> <span class="review"></span> </p><p>6. <span class="math-tex">\(P((A\cup B)')\)</span> = <input type="text" style="height: auto;" data-c="0.189"> <span class="review"></span> </p><p>7. <span class="math-tex">\(P(A\cap B')\)</span> = <input type="text" style="height: auto;" data-c="0.472"> <span class="review"></span> </p><p>8. <span class="math-tex">\(P(B|A')\)</span> = <input type="text" style="height: auto;" data-c="0.545"> <span class="review"></span> </p><p>9. Are events A and B mutually exclusive? Enter Y or N <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> </p><p>10. Are events A and B independent? Enter Y or N <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> </p></div><div class="q-explanation"><p>All answers rounded to 3sf.</p><p>1. 31/53 = 0.585 (31 elements in set A out of a total of 53 elements all together)</p><p>2.43/53 = 0.811 (The union includes everything in A <strong>OR</strong> B - careful not to count the 6 twice)</p><p>3. 6/53 = 0.113 (The intersection, in set A <strong>AND</strong> B)</p><p>4. 6/18 = 0.333 (Of the 18 elements in set B, 6 also belong to set A)</p><p>5. 35/53 = 0.660 (35 of the 53 elements are NOT in set B)</p><p>6. 10/53 = 0.189 (10 out of the 53 elements are NOT in the union of A and B)</p><p>7. 25/53 = 0.472 (25 elements are in the set A AND NOT B)</p><p>8. 12/22 = 0.545 (of the 22 elements that are NOT in set A, 12 are in set B)</p><p>9. N - it is possible to be in both sets</p><p>10. N - <span class="math-tex">\(P(A)\)</span> = 0.585 and <span class="math-tex">\(P(A|B)\)</span> = 0.333 Likelihood of A depends on membership of B</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider two events A and B, <span class="math-tex">\(P(A)\)</span> = 0.3, <span class="math-tex">\(P(B)\)</span> = 0.4 and <span class="math-tex">\(P(A\cup B)\)</span> = 0.58</p></div><div class="q-answer"><p>Work out the value of <span class="math-tex">\(P(A\cap B)\)</span> (exact value) <input type="text" style="height: auto;" data-c="0.12"> <span class="review"></span> </p><p>As such, state whether or not events A and B are </p><p>i) Mutually exclusive <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> (enter Y or N)</p><p>ii) Indepdendent <input type="text" style="height: auto;" data-c="Y"> <span class="review"></span> (enter Y or N)</p></div><div class="q-explanation"><p>Part 1 - For combined events</p><p><span class="math-tex">\(P(A\cup B)\quad =\quad P(A)\quad +\quad P(B)\quad -\quad P(A\cap B)\\ So,\quad 0.58\quad =\quad 0.3\quad +\quad 0.4\quad -\quad P(A\cap B)\\ So\quad P(A\cap B)\quad =\quad 0.12\)</span></p><p>i) No - For mutually exclusive events <span class="math-tex">\(P(A\cap B)\)</span> = 0</p><p>ii) Yes - For independent events....</p><p><span class="math-tex">\(\\ P(A\cap B)\quad =\quad P(A)\quad \times \quad P(B)\\ in\quad this\quad case\\ 0.12\quad =\quad 0.3\quad \times \quad 0.4\)</span></p><p>NOTE - you would be expected to give this reasoning to get these marks.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/LSP/PB/esq1.jpg" style="width: 700px; height: 363px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592636073"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/LSP/PB/esq2.jpg" style="width: 700px; height: 348px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592636517"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/LSP/PB/esq3.jpg" style="width: 700px; height: 238px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592636871"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 4</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/LSP/PB/esq4.jpg" style="width: 700px; height: 938px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592637490"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 5</p> </div> </div> <div class="panel-body"> <p><img alt="" src="../../files/LSP/PB/esq5.jpg" style="width: 700px; height: 903px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/592637928"></iframe></div> </section> </div> <div class="panel panel-default panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 6</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr"><span id="docs-internal-guid-a021702e-7fff-1925-2d11-dbc113b93fa3">Ross and Dylan are playing padel. The probability that Dylan wins the first game is 0.6. If Ross wins the game the probability that he wins the next game is 0.9. If Dylan wins the game, the probability that he wins the next game is 0.5. Let R be the probability that Ross wins a game, and D be the probability that Dylan wins the game. </span></p> <p dir="ltr"><span id="docs-internal-guid-a021702e-7fff-1925-2d11-dbc113b93fa3"><img height="270" src="../../../LmOBvr6yPsGOC1Gwcq6n7S4me2piudKNhC3DoEbPW8DkaIC4EQsOQIIf3BrTe1JG7I-hhhUQE75MYtx0p6jeeYqaQsQa0WyNTFF-9rqiEXqBOU_xvdLCBD5nYuwogdKUPzeOiV53" style="margin-top:0px;" width="273"></span></p> <p dir="ltr" role="presentation"><span id="docs-internal-guid-a021702e-7fff-1925-2d11-dbc113b93fa3">a. Complete the tree diagram to represent the padel game. </span><span id="docs-internal-guid-a021702e-7fff-1925-2d11-dbc113b93fa3"></span></p> <p dir="ltr" role="presentation"><span>b. Find the probability that Dylan wins both games</span><span id="docs-internal-guid-a021702e-7fff-1925-2d11-dbc113b93fa3"></span></p> <p dir="ltr" role="presentation"><span>c. Find the probability that Ross wins the second game, given that he wins the first game.</span></p> <p dir="ltr" role="presentation">Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p> </p> </section> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> <p> </p> <div class="panel-footer"> <div> </div> </div> </div> </div> <div class="panel-footer"> <div><br> <span id="cke_bm_805E" style="display: none;"> </span></div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="2258"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>4.5 & 4.6 Probability</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " 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