Peter guesses on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices, and Peter needs to get at least 7 questions correct to pass. Here are some probabilities computed using the binomial formula: P (getting exactly 7 correct) = 0.0031 P (getting exactly 8 correct) = 0.000386 P (getting exactly 9 correct) = 2.86 * 10-5 P (getting exactly 10 correct) = 9.54 * 10-7 Using the information on the left, combine the individual probabilities to compute the probability that Peter will pass the quiz.

Question

Mathematics

Maeve Odonnell

5 March, 17:11

Peter guesses on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices, and Peter needs to get at least 7 questions correct to pass. Here are some probabilities computed using the binomial formula: P (getting exactly 7 correct) = 0.0031 P (getting exactly 8 correct) = 0.000386 P (getting exactly 9 correct) = 2.86 * 10-5 P (getting exactly 10 correct) = 9.54 * 10-7 Using the information on the left, combine the individual probabilities to compute the probability that Peter will pass the quiz.

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Answers (2)

Know the Answer?

Lena Townsend · Answer 1

The answer is C. 0.0035

Lorelei Lynn · Answer 2

The condition is that he needs to get at least 7 questions correct to pass. We simply have to add all the probabilities that he will get 7, 8, 9, and 10 questions correctly. So,

P = 0.0031 + 0.000386 + 2.86 * 10-5 + 2.86 * 10-5 + 9.54 * 10-7

Then, solve for P.