Richard has been given a 10-question multiple-choice quiz in his history class.

Question

Richard has been given a 10-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 10 questions, find the probability that he will answer no more than 2 questions correctly. Round your answer to the nearest thousandth.

Explanation / Answer

P(correct answer) = 1/4 = 0.25

n = 10

P(X = x) = 10Cx * 0.25x * (1 - 0.25)10-x

P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

              = 10C0 * 0.250 * 0.7510 + 10C1 * 0.251 * 0.759 + 10C2 * 0.252 * 0.758

              = 0.526

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