Easy #4

Probability Level 3

In Mrs Atkins' class, every student swims or cycles and half the students do both. The total number of students who swim is the same as the total number of students who cycle. If $24$ students in total swim, how many students are in Mrs Atkins' class?

The answer is 32.

1 solution

Brian Charlesworth
Jul 27, 2014

In general we have that $n(A \cup B) = n(A) + n(B) - n(A \cap B)$ . Now let $A$ represent the set of students who swim and $B$ the set of students who cycle. Then we are given that $n(A) = n(B) = 24$ , and that $n(A \cap B) = \frac{1}{2} * n(A \cup B)$ . We can then conclude that

$\frac{3}{2} * n(A \cup B) = 48$ , and so $n(A \cup B) = \boxed{32}$ .

Easy #4

The answer is 32.

1 solution

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