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

What are the answer to chose from

Answer 2

Answer:

0.32

Step-by-step 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,

$P(B|A)=\frac{0.08}{0.25}$

$P(B|A)=0.32$

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