A survey of athletes at a high school is conducted, and the following facts are discovered: 68% of the athletes are football players, 26% 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

71% probability that the athlete is either a football player or a basketball player

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that an athlete is a football player.

B is the probability that an athlete is a basketball players.

We have that:

In which a is the probability that an athlete plays football but not basketball and is the probability that an athlete plays both these sports.

By the same logic, we have that:

23% of the athletes play both football and basketball.

This means that

26% are basketball players

This means that . So

68% of the athletes are football players

This means that . So

What is the probability that the athlete is either a football player or a basketball player

71% probability that the athlete is either a football player or a basketball player

final answer is : )