Question

A school choir has 80 students; 36 of them are in seventh grade. Also, 40 students in the choir are girls; 18 of them are in seventh grade. What is the probability that a student picked at random from the choir is either a girl or is in seventh grade?

A.
`27/40`

B.
`29/40`

C.
`13/40`

D.
`33/40`

Answer 1

B. `29/40`

Explanation:

These events are not mutually exclusive. This means they can happen at the same time.

For two events A and B that are not mutually exclusive,

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

Our events are:

P(girl or 7th grade) = P(girl)+P(7th grade)-P(girl and 7th grade)

There are 40 girls out of 80 students:

P(girl or 7th grade) = 40/80+P(7th grade)-P(girl and 7th grade)

There are 36 7th graders in the choir out of 80 students:

P(girl or 7th grade) = 40/80+36/80-P(girl and 7th grade)

There are 18 7th grade girls in the choir:

P(girl or 7th grade) = 40/80+36/80-18/80 = 76/80-18/80 = 58/80

Both the numerator and denominator are divisible by 2:

(58÷2)/(80÷2) = 29/40

Answer 2

B. 29/40

40-18=22
22+36=58/80
58/2=29
80/2=40