If a student randomly guess on 5 multiple choice questions, and each question has 4 possible answers, find the probability that the student gets exactly 3 correct.

Question

anonymous · Answer

(5C3)(0.25^3)(0.75^2) = 0.0879

anonymous · Answer

Could you explain in detail, because i'm having trouble answering these type of questions..

anonymous · Answer

the number of trials would be 5 ? and the number of success is 3 ?

anonymous · Answer

ok.
the probability of success per question, p = 1/4 = 0.25
the probabiity of failure per question is q = 1-p = 0.75

the probability of success three times is p^3 = 0.25^3
the probability that he fails the other 2 times is q^2 = 0.75^2

we multiply by 5C3 because we dont care which 3 he answers correctly.

anonymous · Answer

Thanks a lot !