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
The probability that a student participates in both sports and music is 108/1376
The given parameters are:
Total = 1376
Sport = 649
Music = 433
P(Sport or Music) = 974/1376
The required probability is:
P(Sport and Music) = P(Sport) + P(Music) - P(Sport or Music)
This gives
P(Sport and Music) = 649/1376 + 433/1376 - 974/1376
Evaluate the expression
P(Sport and Music) = 108/1376
Hence, the probability that a student participates in both sports and music is 108/1376
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