A survey of athletes at a high school is conducted, and the following facts are discovered:
of the athletes are football players, are basketball players, and 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?
Enter your answer as a percentage.

Ask by Cook Patel. in the United States

Mar 08,2025

Question

A survey of athletes at a high school is conducted, and the following facts are discovered:
of the athletes are football players, are basketball players, and 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?
Enter your answer as a percentage.

Ask by Cook Patel. in the United States

Mar 08,2025

UpStudy AI · Accepted Answer

Let $$ F $$ be the event that an athlete is a football player and $$ B $$ be the event that an athlete is a basketball player. We are given:

- $$ P(F) = 20\% = 0.20 $$
- $$ P(B) = 35\% = 0.35 $$
- $$ P(F \cap B) = 4\% = 0.04 $$

We want to find $$ P(F \cup B) $$, which represents the probability that an athlete is either a football player or a basketball player.

Using the formula for the union of two events:

$$
P(F \cup B) = P(F) + P(B) - P(F \cap B)
$$

Substitute the given probabilities into the formula:

$$
P(F \cup B) = 0.20 + 0.35 - 0.04
$$

Perform the arithmetic:

$$
P(F \cup B) = 0.55 - 0.04 = 0.51
$$

Thus, the probability in percentage is:

$$
51\%
$$
The probability that a randomly chosen athlete is either a football player or a basketball player is 51%.