Question

at a high school, the probability that a student is a senior is 0.25. the probability that a student plays a sport is 0.20. the probability that a student is a senior and plays a sport is 0.08. what is the probability that a randomly selected student plays a sport, given that the student is a senior?

Answer 1

0.32

Explanation:

We have been given that at a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.20. The probability that a student is a senior and plays a sport is 0.08.

We will use conditional probability formula to solve our given problem.
`P(B|A)=\frac{P(\text{A and B)}}{P(A)}`, where,

`P(B|A)` = The probability of event B given event A.

`P(\text{A and B)}` = The probability of event A and event B.

`P(A)` =Probability of event A.

Let A be that the student is senior and B be the student plays a sport.

P(A and B) = Probability that student is a senior and plays a sport.

`P(B|A)=\frac{\text{Probability that a student is a senior and plays a sport}}{\text{Probability that a student is senior}}`

Upon substituting our given values we will get,

`P(B|A)=(0.08)/(0.25)`

`P(B|A)=0.32`

Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.32.