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Each question of a 5-question multiple choice exam has 3 possible answers. Suppose a student picks an answer at
random for each question. Find the probability the student selects the correct answer on none of the questions.
The probability that none of the questions are answered correctly is
(Simplify your answer. Type an integer or a fraction.)

Ask by Floyd Weaver. in the United States
Jan 22,2025

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The probability that the student selects the correct answer on none of the questions is .

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The Deep Dive

To find the probability that a student selects the correct answer on none of the questions, we start by noting that each question has 3 possible answers, with only 1 correct answer. Thus, the probability of picking an incorrect answer for a single question is .
Since there are 5 questions, and assuming that the student’s choices are independent, we raise the probability of getting an incorrect answer to the power of the number of questions:
Calculating this gives:
So, the probability that the student selects the correct answer on none of the questions is .

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