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

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

Step-by-step explanation:

It is given that,

A suburban high school has a population of 1376 students.

Let the event A be the no. of students participated in sports. Let the event B be the no. of students participated in music.

The number of students who participate in sports is 649.

The number of students who participate in music is 433.

To find the probability of event A (sports):

P (sports) = No. of students participated in sports / Total students.

⇒ 649 / 1376

∴ P (A) = 649 / 1376

To find the probability of event B (music):

P (music) = No. of students participated in music / Total students.

⇒ 433 / 1376

∴ P (B) = 443 / 1376

From the question, we know that the probability that a student participates in either sports or music is 974 / 1376.

∴ P (A∪B) = 974 / 1376

To find the probability that a student participates in both sports and music:

The formula used here is,

P (A∩B) = P (A) + P (B) - P (A∪B)

⇒ 649 / 1376 + 433 / 1376 - 974 / 1376

⇒ 108 / 1376

∴ P (A∩B) = 108 / 1376