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A quiz consists of 12 multiple-choice questions. Each question has 5 possible answers, only one of...

A quiz consists of 12 multiple-choice questions. Each question has 5 possible answers, only one of which is correct. Klein plans to guess the answer to each question. Find the probability that Klein gets exactly 7 correct answers. *
Math   Statistics-And-Probability   
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Answer #1

As each question has 5 choices and only one of them is correct, so probability of getting the correct answer for a given question is - p = 1/5.

Let 'X' be the random variable representing the number of multiple-choice questions Klein gets correct. As each question can be guessed correctly independent of others with equal probability of 'p = 1/5 = 0.2' so the distribution of 'X' will be binomial with parameter n = 12 and p = 0.2 given as -

Thus, for n = 12, r = 7 and p = 0.2 we get -

Probability of getting exactly 7 correct answers is -

Thus, the required probability = 0.0033.

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