Multiple-choice questions each have 5 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 (x

c., where c denotes a correct answer and w denotes a wrong answer.

Question

Franco Spears

Mathematics

13 September, 04:16

Multiple-choice questions each have 5 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 (x

c., where c denotes a correct answer and w denotes a wrong answer.

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Answers (1)

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Opie · Answer 1

Independent Multiplication Rule:

P (X = w, w, w, c) = P (w) ∩ P (w) ∩ P (w) ∩ P (c)

Therefore,

P (X = w, w, w, c) = (1/5) • (1/5) • (1/5) • (1/5)

P (X = w, w, w, c) = 1 / (5^4) = 1/625 or 0.16%