Question

A survey of athletes at a high school is conducted, and the following facts are discovered: 57% of the athletes are football players, 24% are basketball players, and 23% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?

Answer 1

Let A : event that a randomly chosen athlete is a football player

Let B : event that a randomly chosen athlete is a basketball player

P(A) = 0.57             (57%)

P(B) = 0.24              (24%)

P(A AND B) = 0.23              (23% are both football and basketball players)

To find

P(randomly chosen athlete is either a football player or a basketball player)

= P(A OR B)

= P(A) + P(B) - P(A AND B)

= 0.57 + 0.24 - 0.23

= 0.58

P(randomly chosen athlete is either a football player or a basketball player) = 0.58