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289 lines
10 KiB
HTML
289 lines
10 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/activity/dice-experiment-1.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:42:02 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Activity: An Experiment with a Die</title>
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<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: An Experiment with a Die</h1>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>
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<p>You will need:</p>
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<ul>
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<li>A single <a href="../geometry/fair-dice.html">die</a></li>
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</ul></td>
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<td> </td>
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<td><img src="../geometry/images/single-die.svg" alt="single die" height="104" width="113"></td>
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<td> </td>
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</tr>
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</tbody></table>
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<div class="words">
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<h3>Interesting point</h3>
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<p>Many people think that one of these cubes is called "a dice". But no!</p>
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<p>The <b>plural is dice</b>, but the singular is <b>die</b>. (i.e. 1 die, 2 dice.)</p>
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</div>
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<p>The common die has six faces:</p>
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<p class="center"><img src="images/dice2.gif" alt="dice faces 1 to 6" height="61" width="297"></p>
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<p class="center">We usually call the faces 1, 2, 3, 4, 5 and 6.</p>
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<h2>High, Low, and Most Likely</h2>
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<p><b>Question: If you roll a die:</b></p>
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<ul>
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<li>1. What is the <b>least</b> possible score?</li>
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<li>2. What is the <b>greatest</b> possible score?</li>
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<li>3. What do you think is the <b>most likely</b> score?</li>
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</ul>
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<div class="center80">
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<p>The first two questions are quite easy to answer:</p>
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<ul>
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<li>1. The <b>least</b> possible score must be <b>1</b></li>
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<li>2. The <b>greatest</b> possible score must be <b>6</b></li>
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<li>3. The <b>most likely</b> score is ... ???</li>
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</ul>
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<p>Are they all just as likely? Or will some happen more often?</p>
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</div>
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<p>Let us see which is most likely ...</p>
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<h2>The Experiment</h2>
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<div class="center80">
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<p class="center larger"><b>Throw</b> a die 60 times,<br>
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<b>record</b> the scores in a tally table.</p>
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</div>
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<p>You can record the results in this table using <a href="../data/tally-marks.html">tally marks</a>:</p>
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<table align="center" cellpadding="5" border="1">
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<tbody>
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<tr style="text-align:center;">
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<td class="larger"> Score</td>
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<td class="larger" width="300">Tally</td>
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<td class="larger">Frequency</td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">1</td>
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<td> </td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">2</td>
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<td style="width:300px;"> </td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">3</td>
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<td style="width:300px;"> </td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">4</td>
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<td style="width:300px;"> </td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">5</td>
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<td style="width:300px;"> </td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">6</td>
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<td style="width:300px;"> </td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td> </td>
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<td align="right" width="300">Total Frequency = </td>
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<td class="larger">60</td>
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</tr>
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</tbody></table>
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<p class="largest">OK, Go!</p>
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<p class="center">... ...</p>
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<p class="center">... ...</p>
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<p class="center">... ...</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/die-results-empty.gif" alt="die results empty" height="208" width="300"></p>
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<p><b>Finished ...?</b></p>
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<p>Now draw a bar graph to illustrate your results.</p>
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<p>You can make your own.</p>
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<p>Or you can use <a href="../data/data-graph.html">Data Graphs (Bar, Line and Pie)</a> then print it out.</p>
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<div style="clear:both"></div>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/die-results.gif" alt="die results" height="152" width="220"></p>
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<p>You may get something like this:</p>
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<div style="clear:both"></div>
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<div class="center80">
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<ul>
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<li>Are the bars all the same height?</li>
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<li>If not ... why not?</li>
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</ul>
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</div>
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<h2>60 Throws</h2>
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<p>OK, why did I ask you to make <b>60</b> throws? Well, 6 throws is not enough for good results. 600 will give good results but is a lot of work. So 60 seems OK, and is also <b>10 lots of 6</b>.</p>
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<p>So we should <b>expect</b> <b>10</b> of each number, like this:</p>
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<p class="center"><img src="images/die-results-theory.gif" alt="die results theory" height="207" width="300"><br>
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<br>
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Those are the <b>theoretical</b> values,<br>
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as opposed to the <b>experimental</b> ones you got from your <b>experiment</b>!<br>
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</p>
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<div class="center80">
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<p class="center larger">How do those theoretical results compare with your experimental results?</p>
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</div>
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<p>This graph and your graph should be <b>similar</b>, but they are not likely to be exactly the same, as your experiment relied on <b>chance</b>, and the number of times you did it was fairly small.</p>
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<p>If you did the experiment a very large number of times, you would get results much closer to the theoretical ones.</p>
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<h2>Questions</h2>
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<ul>
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<div class="bigul">
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<li>Which face came up most often? ____</li>
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<li>Which face came up least often? ____</li>
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<li>Do you think you would get the same results if you did this again? Yes / No</li>
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</div>
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</ul>
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<div class="center80">
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<p class="larger">An experiment gives results.</p>
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<p class="larger">When done again it may give <b>different</b> results!</p>
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<p class="larger">So it is important to know when results are <b>good quality</b>, or just <b>random</b>.</p>
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</div>
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<h2>Probability</h2>
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<p>On the page <a href="../data/probability.html">Probability</a> you will find a formula:</p>
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<p class="center">Probability of an event happening = <span class="intbl"><em>Number of ways it can happen</em><strong>Total number of outcomes</strong></span></p>
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<div class="example">
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<h3>Example: Probability of a 2</h3>
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<p>We know there are 6 possible outcomes.</p>
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<p>And there is only 1 way to get a 2.</p>
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<p>So the probability of getting 2 is:</p>
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<p class="center larger">Probability of a 2 = <span class="intbl"><em>1</em><strong>6</strong></span></p>
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</div>
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<p>Doing that for each score gets us:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td style="width:100px;"> Score</td>
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<td style="width:100px;">Probability</td>
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</tr>
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<tr style="text-align:center;">
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<td>1</td>
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<td>1/6</td>
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</tr>
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<tr style="text-align:center;">
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<td>2</td>
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<td>1/6</td>
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</tr>
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<tr style="text-align:center;">
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<td>3</td>
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<td>1/6</td>
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</tr>
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<tr style="text-align:center;">
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<td>4</td>
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<td>1/6</td>
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</tr>
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<tr style="text-align:center;">
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<td>5</td>
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<td>1/6</td>
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</tr>
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<tr style="text-align:center;">
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<td>6</td>
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<td>1/6</td>
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</tr>
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<tr style="text-align:center;">
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<td> </td>
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<td class="larger">Total = 1</td>
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</tr>
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</tbody></table>
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<p class="center larger">The sum of all the probabilities is <b>1</b></p>
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<div class="center80">
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<p class="center">For any experiment:</p>
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<p class="center">The sum of the probabilities of <b>all</b> possible outcomes is always equal to <b>1</b></p>
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</div>
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<p> </p>
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<div class="related">
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<a href="dice-experiment-2.html">An Experiment with 2 Dice</a>
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<a href="../data/index.html">Data Index</a>
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<a href="../geometry/fair-dice.html">Fair Dice</a>
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</div>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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