Question

A student ran out of time on a multiple-choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices –a,b,c,d – and only one correct answer. What is the probability that he answered both of the problems correctly?

Do not round your answer.

Answer 1

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The probability of answering a single problem correctly by randomly guessing is 1/4, since there are 4 answer choices and only one correct answer. Since the student randomly guessed the answer to both problems, the probability of answering both problems correctly is:

(1/4) x (1/4) = 1/16

Therefore, the probability that the student answered both problems correctly is 1/16.