multiplication probability

Question

Multiple-choice questions each have 6 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 , where C denotes a correct answer and W denotes a wrong answer. (round answer to 4 decimal places)  What is the probability of getting exactly one correct answer when 4 guesses are made? (round answer to 4 decimal places) P(exactly one correct answer) = 

Answer 1

Cody,

The probability of the good answer is 1/6. The probability of a wrong answer is 5/6. Therefore:

P(WWWC) = (5/6)(5/6)(5/6)(1/6) = 0.0965

The probability of getting exactly one correct answer out of 4 attempts is possible in 4 ways.

The first is correct and all others are wrong OR the second correct and all others are wrong OR the third is correct and all others are wrong OR the fourth is correct and all others are wrong.

CWWW or WCWW or WWCW or WWWC

All 4 have the same probability, so the final answer is 4 *0.0965=0.3858