Multiple-choice questions each have 5 possible answers, one of which is correct.

Question

Multiple-choice questions each have 5 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)=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) =

Explanation / Answer

P(correct answer) = 1/5

P(Wrong answer) = 4/5

Hence,

P(WWWWC) = (4/5)4 * (1/5) = 0.0819

Also,

P(Exactly one correct answer) = 5*P(WWWWC) [Since any of the 5 answers can be correct so 5 possibilities]

P(Exactly one correct answer) = 5*0.0819 = 0.4096

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