Question

Multiple-choice questions each have 3 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.

Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC)P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.
(round answer to 4 decimal places)
P(WWWWC)=

What is the probability of getting exactly one correct answer when 5 guesses are made?
(round answer to 4 decimal places)
P(exactly one correct answer) =

Answer 1

Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct.

For a single problem there are 3 options out of which only one is correct. Hence the probability of a single question being correct is ,

P(C) = 1/3

P(W) = 2/3

Hence the required probability would be given by,

What is the probability of getting exactly one correct answer when 5 guesses are made?

The probability of exactly one correct answer would be given by,