Question

A suburban high school has a population of 1376 students. The number of students who participate in sports us 649. The number of students who participate in music is 433. If the probability that a student participates in either sports is 974/1376, what is the probability that a student participates in both sports and music?

Answer 1

The probability that a student participates in both sports and music is 108/1376

Explanation:

Let x be the number of students participating in both sports and music

According to the question:

P(A or B) = P(A) + P(B) - P(A and B)

P(sports or music) = P(sports) + P(music) - P(sports and music)

$\frac{974}{1376} = \frac{649}{1376} + \frac{433}{1376} - \frac{x}{1376} \\\\974 = 1082 - x\\\\x = 108$

P(sports and music) = $\frac{108}{1376}$

Therefore, the probability that a student participates in both sports and music is 108/1376