SOLUTION: If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions: What is the probability of getting 9 correct?

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Question 1199511: If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions:
What is the probability of getting 9 correct?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The number of ways of "choosing" 9 of the 16 questions to be the ones that are answered correctly is C(16,9) = "16 choose 9".

For each of those ways, the probability of 9 right and 7 wrong is (1/4)^9 * (3/4)^7.

ANSWER: (use a calculator....)

C%2816%2C9%29%2A%281%2F4%29%5E9%2A%283%2F4%29%5E7

Answer the other several questions you have submitted the same way.

For a question like "getting AT LEAST" 6 right, you will need to perform the calculations for 6, 7, 8, ..., and 16 right and add the probabilities for the separate cases. That is a huge amount of work; most good calculators like a TI-84 have built-in capabilities for getting the answer with a few quick inputs.