If a student randomly guesses at 15 multiple-choice questions, find the probability that the student gets exactly seven correct. Each question has four possible choices

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1. for any question,
prob(correct guess) = 1/4
prob(wrong guess) = 3/4

To have exactly 7 of 15 correct,
prob = C(15,7)((1/4)^7 (3/4)^8
= 6435 (1/16384)(6561/65536)
= appr .039

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2. If a student randomly guesses at 15 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.

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3. If a student randomly guesses at 14 multiple-choice questions, find the probability that the student gets exactly five correct. Each question has five possible choices.

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