Question

In Miss Smith's class, 24 out of 30 students passed the last test, in Mr. Greenes class, 21 out of 28 students passed the last test. If you selected one student from each class, what is the probability that one would have passed and one would have failed? Please show your work.

Answer 1

Let S be the event that a student in Miss Smith's class failed.

P(S) = (30-24)/30 = 6/30 = 0.2 ; P(S') = 1 - P(S) = 1 - 0.2 = 0.8

Let G be the event that a student in Mr. Greenes' class failed.

P(G) = (28-21)/28 = 7/28 = 0.25 ; P(G') = 1 - P(G) = 1 - 0.25 = 0.75

One student is picked from each class.

It is clear that S and G are independent events.

Thus ; probability that one student would have passed and one student would have failed

= P(S'G) + P(SG') = P(S')P(G) + P(S)P(G') = 0.80.25 + 0.20.75 = 0.2 + 0.15 = 0.35