Question

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices – a, b, c, d, e – and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer.

Answer 1

When doing a compounding probability problem, you should consider what the odds of success for a certain action. In this case, we know that a correct answer only appears in one of the 5 options, giving a 20% chance to guess it randomly, knowing this we can find out that the odds of guessing incorrectly are 80%, as it is the inverse of a correct answer. In order to find the odds of guessing incorrectly twice, we can simply form 80% as a fraction (4/5) and multiply it by a second incorrect guess (4/5) so we get 4/5 * 4/5 = 16/25 or 64%.
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