108 / 1376 is the probability that a student participates in both sports and music.
<u>Step-by-step explanation:</u>
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.
<u>To find the probability of event A (sports) :</u>
P(sports) = No.of students participated in sports / Total students.
⇒ 649 / 1376
∴ P(A) = 649 / 1376
<u>To find the probability of event B (music) :</u>
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
<u>To find the probability that a student participates in both sports and music :</u>
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
