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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 neither of the problems correctly?Write your answer as a fraction in simplest form.

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 neither of the problems correctly?Write your answer as a fraction in simplest form.

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Solution

The probability of guessing one question correctly is 1/4, since there are 4 possible answers and only one is correct. Therefore, the probability of guessing one question incorrectly is 1 - 1/4 = 3/4.

Since the two questions are independent events, the probability of guessing both questions incorrectly is the product of the probabilities of guessing each question incorrectly.

So, the probability of guessing both questions incorrectly is (3/4) * (3/4) = 9/16.

This problem has been solved

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