Question

A high school class consists of 7 ​seniors, 10 ​juniors, 12 ​sophomores, and 11 freshmen. Exactly 4 of the juniors are female​, and exactly 2 of the sophomores are male. If two students are randomly selected from this​ class, what is the probability that the pair consists of a male junior and a female ​sophomore?

Answer 1

1/13

Explanation:

There exactly 7 seniors 10 Juniors, 12 sophomores and 11 freshman

in which 4 of the juniors are Female , and exactly 2 of the sophomores are male. Therefore,

10-4= 6 juniors are male

12-2 = 10 female sophomores

Total = 7+10+12+11= 40 students

P(male junior then female soph.)=
`(6)/(40)*(10)/(39)= (1)/(26)`

P(female soph then male junior)=
`(10)/(40)*(6)/(39)= (1)/(26)`

Therefore the final answer will be = 1/26 +1/26= 1/13