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. [tex]P(B|A)=\frac{P(\text{A and B)}}{P(A)}[/tex], where,
[tex]P(B|A)[/tex] = The probability of event B given event A.
[tex]P(\text{A and B)}[/tex] = The probability of event A and event B.
[tex]P(A)[/tex] =Probability of event A.
Let A be that the student is senior and B be the student plays a sport. Â
P(A and B) = Probability that student is a senior and plays a sport.
[tex]P(B|A)=\frac{\text{Probability that a student is a senior and plays a sport}}{\text{Probability that a student is senior}}[/tex]
Upon substituting our given values we will get,
[tex]P(B|A)=\frac{0.08}{0.25}[/tex]
[tex]P(B|A)=0.32[/tex]
Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.32.
