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    <name>
      <text>35.4.4.2 Duration of employment</text>
    </name>
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      <text><![CDATA[<h4 class="HELM_exercise"> Exercise </h4>
<p>The table below show the number of complete years a group of people have been working in
their current employment. \[ {@tb@} \] </p>
<p> An employee is selected at random. What are the probabilities of the following events: </p>
<ol class="HELM_parts">
<li> \(A = \{\text{the person is in the group with the highest count}\}\); </li>
<li> \(B = \{\text{the person has been working there for less than 4 years}\}\); </li>
<li> \(C = \{\text{the person has been working there for at least 8 years}\}\). </li>
</ol>
<p> Give all probabilities as fractions, rather than decimals: </p>
<ol class="HELM_parts">
<li> \(\mathbb{P}(A)=\quad\)[[input:ans1]][[validation:ans1]][[feedback:prt1]] </li>
<li> \(\mathbb{P}(B)=\quad\)[[input:ans2]][[validation:ans2]][[feedback:prt2]] </li>
<li> \(\mathbb{P}(C)=\quad\)[[input:ans3]][[validation:ans3]][[feedback:prt3]] </li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<h4 class="HELM_solution"> Solution </h4>
<p>&nbsp;\[ {@tb@} \]<br></p><p>From the above table we see that the total number of employees is \({@enn@}\). The probabilities, therefore, come directly from the table: </p>
<ol class="HELM_parts">
<li> \(\mathbb{P}(A) = \displaystyle {@ta1@}\) </li>
<li> \(\mathbb{P}(B) = \dfrac{{@p01@} + {@p23@}}{@enn@}=\displaystyle {@ta2@}\) </li>
<li> \(\mathbb{P}(C) =\dfrac{{@p811@} +{@p12@}}{@enn@} = \displaystyle {@ta3@}\) </li>
</ol>]]></text>
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      <text>2021072200</text>
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      <text><![CDATA[p01: 15 + rand(6);
p23: 10 + rand([1,2,3,4]);
p45: rand([8,9]);
p67: rand([5,6,7]);
p811: rand([5,6,7]);
p12: rand([1,2,3]);
enn: p01 + p23 + p45 + p67 + p811 + p12;
tb: table(["Years of employment","Number of people"],["0 or 1 year",p01],["2 or 3 years",p23],["4 or 5 years",p45],["6 or 7 years",p67],["8 to 11 years",p811],["12 or more years",p12]);
ta1: p01 / enn;
ta2: (p01 + p23) / enn;
ta3: (p811 + p12) / enn;]]></text>
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      <text>\[ \mathbb{P}(A) = {@ta1@} \]
\[ \mathbb{P}(B) = {@ta2@} \]
\[ \mathbb{P}(C) = {@ta3@} \]</text>
    </questionnote>
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      <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>
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