Question

If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.

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Answer #1

X ~ Binomial (n,p)

Where n = 20 , p = 1/4 = 0.25 (Probability of one correct out of four choices)

Binomial probability distribution is

P(X) = nCx px ( 1 - p)n-x

P( X = 4) = 20C4 0.254 0.7516

= 0.1897

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