Conditional Probability Math Example 1

Follow the full solution, then compare it with the other examples linked below.

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In a class of

30

students,

18

play soccer,

12

play basketball, and

6

play both. If a student plays soccer, what is the probability they also play basketball?

1
We need $P(B \mid S) = \frac{P(B \cap S)}{P(S)}$ .
2
$P(B \cap S) = \frac{6}{30} = \frac{1}{5}$ and $P(S) = \frac{18}{30} = \frac{3}{5}$ .
3
$P(B \mid S) = \frac{1/5}{3/5} = \frac{1}{3}$ .

Answer

P(B \mid S) = \frac{1}{3}

Conditional probability restricts the sample space to only those outcomes where the given condition is true. Here we only consider the

18

soccer players.

About Conditional Probability

The conditional probability $P(A|B)$ is the probability of event $A$ occurring given that event $B$ has already occurred.

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