Question

Multiple-choice questions each have 3 possible answers, one of which is correct. Assume that you guess the answers to 4 such questions.

Use the multiplication rule to find the probability that the first three guesses are wrong and the fourth is correct. That is, find P(WWWC)P(WWWC), where C denotes a correct answer and W denotes a wrong answer.
(round answer to 2 decimal places)
P(WWWC)=P(WWWC)=

What is the probability of getting exactly one correct answer when 4 guesses are made?
(round answer to 2 decimal places)
P(exactly one correct answer) =

Answer 1

a) P(WWWC) = P(W) * P(W) * P(W) * P(C) = (2/3) * (2/3) * (2/3) * (1/3) = 0.10

b) P(exactly one correct answer) = P(WWWC) + P(WWCW) + P(WCWW) + P(CWWW)

                                                    = 4 * (2/3) * (2/3) * (2/3) * (1/3)

                                                    = 0.40