Multiple-choice test probability

Question

A multiple-choice test has 4 choices, one of which is a correct answer. If a student just guesses the answer, what is the probability that he has exactly 1 correct answer in 3 successive unrelated questions?

Answer 1

4 choices, probability of randomly getting 1 correct = 1/4

Pr(all 3 correct) = (1/4)^3 = 1/64

Pr(zero correct) = (3/4)^3 = 27/64

Pr(2 correct) = (1/4)^2(3/4) = 3/64x 3 = 9/64

Pr(1 correct) = (3/4)^2(1/4) = 9/64 x 3 = 27/64

(1+27+9+27)/64 = 64/64 = 1

3 ways to get exactly 1 correct

CNN, NCN, or NNC

each has probability (3/4)(1/4)(1/4) = 3/64

3 x 3/64 = 9/64

Pr(exactly 1 correct in 3 tries) = 9/64 = 14.0625%

= about 14%