Question

www.g A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are football players, 79% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player

Answer 1

84%

Explanation:

The probability that the selected player is a football player, P(F)=19%

The probability that the selected player is a basketball player, P(B)=79%

The probability that the selected player play both football and basketball,

`P(B \cap F)=14\%`

We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player,
`P(B \cup F)`

In probability theory

`P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%`

The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.