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 0.15. 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 senior?
A. 0.10
B. 0.15
C. 0.66
D. 0.40

Please explain

Answer 1

Use the definition of conditional probability:

$P(\text{sports}\mid\text{senior})=\dfrac{P(\text{sports AND senior})}{P(\text{senior})}$

We know that 0.10 of students belong to both categories, and that 0.25 of students are seniors, so

$P(\text{sports}\mid\text{senior})=\dfrac{0.10}{0.25}=0.40$