Question

10.3.23

Answer 1

Answer:

The probability that a high school member selected at random is on the swim team is $\frac{9}{40} = 0.225$

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: High school student.

Event B: Is on the swin team.

Probability of selecting a high school student:

Of the 1500 students, 200 are on high school. So

$P(A) = \frac{200}{1500}$

Probability of selecting a high school student who swims:

Of the 1500 students, 45 are high school students who swim. So

$P(A \cap B) = \frac{45}{1500}$

What is the probability that a high school member selected at random is on the swim team?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{45}{1500}}{\frac{200}{1500}} = \frac{45}{200} = \frac{9}{40} = 0.225$

The probability that a high school member selected at random is on the swim team is $\frac{9}{40} = 0.225$