\( \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & 10 & \\ \hline \text{Girls} & 13 & 16 & \\ \hline \text{total} & & \\ \hline \end{array} \)
Question 1
(a) How many boys are in the class?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & \bbox[yellow,3px]{11} & \bbox[yellow,3px]{10} & \bbox[orange,3px]{21} \\ \hline \text{Girls} & 13 & 16 & \\ \hline \text{total} & & & \\ \hline \end{array} \)
\( \bbox[yellow,3px]{11}+\bbox[yellow,3px]{10} = \bbox[orange,3px]{21} \) boys in the class.
(b) How many girls are in the class?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & 10 & 21 \\ \hline \text{Girls} & \bbox[yellow,3px]{13} & \bbox[yellow,3px]{16} & \bbox[orange,3px]{29} \\ \hline \text{total} & & & \\ \hline \end{array} \)
\( \bbox[yellow,3px]{13}+\bbox[yellow,3px]{16} = \bbox[orange,3px]{29} \) girls in the class.
(c) How many students who can swim are in the class?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & \bbox[yellow,3px]{11} & 10 & 21 \\ \hline \text{Girls} & \bbox[yellow,3px]{13} & 16 & 29 \\ \hline \text{total} & \bbox[orange,3px]{24} & & \\ \hline \end{array} \)
\( \bbox[yellow,3px]{11}+\bbox[yellow,3px]{13} = \bbox[orange,3px]{24} \) swimmers in the class.
(d) How many students cannot swim in the class?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & \bbox[yellow,3px]{10} & 21 \\ \hline \text{Girls} & 13 & \bbox[yellow,3px]{16} & 29 \\ \hline \text{total} & 24 & \bbox[orange,3px]{26} & \\ \hline \end{array} \)
\( \bbox[yellow,3px]{10}+\bbox[yellow,3px]{16} = \bbox[orange,3px]{26} \) non-swimmers in the class.
(e) How many students are in the class?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & 10 & \bbox[yellow,3px]{21} \\ \hline \text{Girls} & 13 & 16 & \bbox[yellow,3px]{29} \\ \hline \text{total} & \bbox[yellow,3px]{24} & \bbox[yellow,3px]{26} & \bbox[orange,3px]{50} \\ \hline \end{array} \)
\( \begin{align} \bbox[yellow,3px]{24}+\bbox[yellow,3px]{26} &= \bbox[orange,3px]{50} \\ \bbox[yellow,3px]{21}+\bbox[yellow,3px]{29} &= \bbox[orange,3px]{50} \end{align} \) students in the class.
(f) How many students are boys or swimmers?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & \bbox[yellow,3px]{11} & \bbox[yellow,3px]{10} & 21 \\ \hline \text{Girls} & \bbox[yellow,3px]{13} & 16 & 29 \\ \hline \text{total} & 24 & 26 & 50 \\ \hline \end{array} \)
\( \bbox[yellow,3px]{11}+\bbox[yellow,3px]{10}+\bbox[yellow,3px]{13} = \bbox[orange,3px]{34} \)
(g) How many students are boys and swimmers?
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & \bbox[orange,3px]{11} & 10 & 21 \\ \hline \text{Girls} & 13 & 16 & 29 \\ \hline \text{total} & 24 & 26 & 50 \\ \hline \end{array} \)
\( \bbox[orange,3px]{11} \)
(h) Find the probability that a randomly chosen student is a girl.
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & 10 & 21 \\ \hline \text{Girls} & 13 & 16 & \bbox[orange,3px]{29} \\ \hline \text{total} & 24 & 26 & \bbox[orange,3px]{50} \\ \hline \end{array} \)
\( \displaystyle \frac{\bbox[orange,3px]{29}}{\bbox[orange,3px]{50}} \)
(i) Find the probability that a randomly chosen student is a non-swimmer.
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & 10 & 21 \\ \hline \text{Girls} & 13 & 16 & 29 \\ \hline \text{total} & 24 & \bbox[orange,3px]{26} & \bbox[orange,3px]{50} \\ \hline \end{array} \)
\( \displaystyle \frac{\bbox[orange,3px]{26}}{\bbox[orange,3px]{50}} = \frac{\bbox[orange,3px]{13}}{\bbox[orange,3px]{25}} \)
(j) Find the probability that a randomly chosen student is a girl who can swim.
\( \require{AMSsymbols} \begin{array}{|c|c|c|c|} \hline &\text{swimmer} &\text{non-swimmer} &\text{total} \\ \hline \text{Boys} & 11 & 10 & 21 \\ \hline \text{Girls} & \bbox[orange,3px]{13} & 16 & 29 \\ \hline \text{total} & 24 & 26 & \bbox[orange,3px]{50} \\ \hline \end{array} \)
\( \displaystyle \frac{\bbox[orange,3px]{13}}{\bbox[orange,3px]{50}} \)
Question 2
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & & 21 & 33 \\ \hline \text{Girls} & 29 & & \\ \hline \text{total} & & & 80 \\ \hline \end{array} \)
(a) How many heavy boys are there?
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & \bbox[orange,3px]{12} & \bbox[yellow,3px]{21} & \bbox[yellow,3px]{33} \\ \hline \text{Girls} & 29 & & \\ \hline \text{total} & & & 80 \\ \hline \end{array} \)
\( \displaystyle \bbox[yellow,3px]{33}-\bbox[yellow,3px]{21}=\bbox[orange,3px]{12} \)
(b) How many heavy students are there?
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & \bbox[yellow,3px]{12} & 21 & 33 \\ \hline \text{Girls} & \bbox[yellow,3px]{29} & & \\ \hline \text{total} & \bbox[orange,3px]{41} & & 80 \\ \hline \end{array} \)
\( \displaystyle \bbox[yellow,3px]{12}+\bbox[yellow,3px]{29}=\bbox[orange,3px]{41} \)
(c) How many light students are there?
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & 12 & 21 & 33 \\ \hline \text{Girls} & 29 & & \\ \hline \text{total} & \bbox[yellow,3px]{41} & \bbox[orange,3px]{39} & \bbox[yellow,3px]{80} \\ \hline \end{array} \)
\( \displaystyle \bbox[yellow,3px]{80}-\bbox[yellow,3px]{41}=\bbox[orange,3px]{39} \)
(d) How many light girls are there?
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & 12 & \bbox[yellow,3px]{21} & 33 \\ \hline \text{Girls} & 29 & \bbox[orange,3px]{18} & \\ \hline \text{total} & 41 & \bbox[yellow,3px]{39} & 80 \\ \hline \end{array} \)
\( \displaystyle \bbox[yellow,3px]{39}-\bbox[yellow,3px]{21}=\bbox[orange,3px]{18} \)
(e) How many girls are there?
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & 12 & 21 & 33 \\ \hline \text{Girls} & \bbox[yellow,3px]{29} & \bbox[yellow,3px]{18} & \bbox[orange,3px]{47} \\ \hline \text{total} & 41 & 39 & 80 \\ \hline \end{array} \)
\( \displaystyle \bbox[yellow,3px]{29}+\bbox[yellow,3px]{18}=\bbox[orange,3px]{47} \)
(f) Find the probability that a randomly chosen student is a girl.
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & 12 & 21 & 33 \\ \hline \text{Girls} & 29 & 18 & \bbox[orange,3px]{47} \\ \hline \text{total} & 41 & 39 & \bbox[orange,3px]{80} \\ \hline \end{array} \)
\( \displaystyle \frac{\bbox[orange,3px]{47}}{\bbox[orange,3px]{80}} \)
(g) Find the probability that a randomly chosen student is a light boy.
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & 12 & \bbox[orange,3px]{21} & 33 \\ \hline \text{Girls} & 29 & 18 & 47 \\ \hline \text{total} & 41 & 39 & \bbox[orange,3px]{80} \\ \hline \end{array} \)
\( \displaystyle \frac{\bbox[orange,3px]{21}}{\bbox[orange,3px]{80}} \)
(h) Find the probability that a randomly chosen student is a girl or a heavy student.
\( \begin{array}{|c|c|c|c|} \hline &\text{Heavy} &\text{Light} &\text{total} \\ \hline \text{Boys} & \bbox[yellow,3px]{12} & 21 & 33 \\ \hline \text{Girls} & \bbox[yellow,3px]{29} & \bbox[yellow,3px]{18} & 47 \\ \hline \text{total} & 41 & 39 & \bbox[orange,3px]{80} \\ \hline \end{array} \)
\( \displaystyle \frac{\bbox[yellow,3px]{12}+\bbox[yellow,3px]{29} +\bbox[yellow,3px]{18}}{\bbox[orange,3px]{80}} = \frac{\bbox[yellow,3px]{59}}{\bbox[orange,3px]{80}} \)
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