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.

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

step-by-step explanation:

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