Question

10.3.23

Question Help
o
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?
The probability is
o
(Simplify your answer.)

Answer 1

The probability that a high school member selected at random is on the swim team is
`(9)/(40) = 0.225`

Explanation:

Conditional Probability

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

`P(B|A) = (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) = (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) = (45)/(1500)`

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

`P(B|A) = (P(A \cap B))/(P(A)) = ((45)/(1500))/((200)/(1500)) = (45)/(200) = (9)/(40) = 0.225`

The probability that a high school member selected at random is on the swim team is
`(9)/(40) = 0.225`