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<quiz>
  <question type="stack">
    <name>
      <text>35.2.3.2 Dice throwing experiment</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h4 class="HELM_exercise"> Exercise </h4>
<p> An experiment consists of throwing two \({@fcs@}\)-faced dice.</p>
<ol class="HELM_parts">
<li> Write down the sample space of one of the die in this experiment. </li>
<li> If \(A\) is the event that the total score is less than \(5\), find \(\text{P}(A)\). </li>
<li> If \(B\) is the event that a double, i.e. \((1,1),(2,2),(3,3),...\), is thrown, find \(\text{P}(B')\). </li>
<li> What is the probability that a double is not thrown and the score is less than \(5\)? The event here is notated \(A\cap B'\), so that the probability we are seeking is \(\text{P}(A\cap B')\).</li>
</ol>
<p> Give all probabilities as fractions, not decimals: </p>
<ol class="HELM_parts">
<li>The sample space of one of the die in this experiment is [[input:ans1]][[validation:ans1]][[feedback:prt1]].</li>
<li> \(\text{P}(A)=\quad\)[[input:ans2]][[validation:ans2]][[feedback:prt2]] </li>
<li> \(\text{P}(B')=\quad\)[[input:ans3]][[validation:ans3]][[feedback:prt3]] </li>
<li> \(\text{P}(A\cap B')=\quad\)[[input:ans4]][[validation:ans4]][[feedback:prt4]] </li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li> The sample space is a set consisting of all pairs \((a,b)\) such that \(a,b\) are elements of \({@ta1@}.\)</li>
    <li>The pairs that make a total score less than \(5\) are \(\{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)\}\) so that \(\text{P}(A)= \dfrac{6}{@fcs^2@} = \displaystyle {@ta2@}.\)</li>
    <li> There are \({@fcs@}\) possible doubles so that \(\text{P}(B) = \dfrac{@fcs@}{@fcs^2@} = \dfrac{1}{@fcs@}\) and therefore \(\text{P}(B')=1 - \left( \dfrac{1}{@fcs@} \right) = \displaystyle {@ta3@}.\)</li>
    <li> The set \(A\cap B'\) consists only of the pairs \((1,2),(1,3),(2,1),(3,1)\) so that \(\text{P}(A\cap B')= \displaystyle {@ta4@}.\)</li>
</ol>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>/* pick a Platonic solid:*/
fcs: rand([4,6,8,12,20]);
ta1: setify(makelist(i,i,1,fcs));
ta2: 6 / (fcs^2);
ta3: 1 - (1/fcs);
ta4: 4 / (fcs^2);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>d\({@fcs@}\):\[\text{P}(A) = {@ta2@}\]
\[ \text{P}(B') = {@ta3@} \]
\[ \text{P}(A\cap B') = {@ta4@} \]</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color: green; --darkreader-inline-color:#72ff72;" data-darkreader-inline-color=""><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color: orange; --darkreader-inline-color:#ffae1a;" data-darkreader-inline-color=""><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color: red; --darkreader-inline-color:#ff1a1a;" data-darkreader-inline-color=""><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
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      <options/>
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    <input>
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      <type>algebraic</type>
      <tans>ta4</tans>
      <boxsize>5</boxsize>
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      <value>1.0000000</value>
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        <text>AR1: sort(args(ev(ans1,simp)));
AS1: sort(args(ans1));</text>
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        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
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          <text/>
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        <falsefeedback format="html">
          <text/>
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        <name>1</name>
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          <text><![CDATA[<p dir="ltr" style="text-align: left;">Please do not write duplicate entries in a set</p>]]></text>
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        <falseanswernote>prt1-3-F</falseanswernote>
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          <text/>
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        <trueanswernote>prt2-1-T</trueanswernote>
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          <text/>
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        <falseanswernote>prt2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
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  </question>
</quiz>
