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You are taking a multiple choice quiz. There are 10 questions. Each question has 4 possible answer choices. You guess on each question.

Determine each probability to 4 decimal places.

A. You get exactly 2 questions correct.

B. You get at most 2 questions correct.

C. You get at least 2 questions correct

User DooBLER
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Final answer:

The probability of getting exactly 2 questions correct on a 10-question multiple choice quiz is 0.2816; at most 2 questions correct is 0.5256; and at least 2 questions correct is 0.9214.

Step-by-step explanation:

The probability of guessing multiple-choice questions on a quiz involves binomial probability. Here, the student guesses on a 10-question multiple-choice quiz with 4 options per question.

A. You get exactly 2 questions correct.

The probability of getting exactly 2 questions correct is calculated by a combination of choosing 2 out of 10 questions times the probability of getting 2 questions right and 8 questions wrong.

Probability = (10 choose 2)*(1/4)^2*(3/4)^8 = 0.2816

B. You get at most 2 questions correct.

This requires the sum of probabilities of getting 0, 1, or 2 questions correct.

Probability = (10 choose 0)*(1/4)^0*(3/4)^10 + (10 choose 1)*(1/4)^1*(3/4)^9 + (10 choose 2)*(1/4)^2*(3/4)^8 = 0.5256

C. You get at least 2 questions correct.

This is 1 minus the probability of getting 0 or 1 question correct.

Probability = 1 - [(10 choose 0)*(1/4)^0*(3/4)^10 + (10 choose 1)*(1/4)^1*(3/4)^9] = 0.9214

User Lee H
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