Question

question 1 of 10
at a high school, the probability that a student is a senior is 0.25. the probability that a student plays a sport is 0.15. the probability that a student is a senior and plays a sport is 0.10.
what is the probability that a randomly selected student plays a sport, given that the student is a senior?
a. 0.10
b. 0.66
c. 0.15
d. 0.40

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\).

Step2: Identify the events

Let \(A\) be the event that a student plays a sport and \(B\) be the event that a student is a senior.
We are given \(P(B) = 0.25\), \(P(A\cap B)=0.10\).

Step3: Substitute the values into the formula

\(P(A|B)=\frac{0.10}{0.25}=\frac{10}{25}=\frac{2}{5} = 0.40\)

Answer:

D. \(0.40\)