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# In a recreation center with 1,500 members, 200 are high school students. Of the members, 300 regularly swim. The 45 students of the high school swim team are all members and practice at the pool every week. What is the probability that a high school member selected at random is on the swim team?

Solution

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We need to find $P(\text{swim team }|\text{ highschool})$.

Use the formula for the conditional probability. For any two events $A$ and $B$, with $P(A)\ne 0$,

$P(B\hspace{1mm}|\hspace{1mm}A)=\dfrac{P(A\text{ and }B)}{P(A)}$

So, we write:

$P(\text{swim team }|\text{ high school})=\dfrac{P(\text{high school}\text{ and }\text{swim team})}{P(\text{high school})}$

From the given, $P(\text{high school})=\dfrac{200}{1500}$ and $P(\text{high school}\text{ and }\text{swim team})=\dfrac{45}{1500}$ so:

$P(\text{swim team }|\text{ high school})=\dfrac{\dfrac{45}{1500}}{\dfrac{200}{1500}}$

$P(\text{swim team }|\text{ high school})=\dfrac{45}{200}=\color{#c34632}{\dfrac{9}{40}}$

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