SOLUTION: A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the stude

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Question 528255: A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers.
(Please answer in simplest terms. I do not know complex probability equations.)
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers.
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Binomial Problem with n = 48 and p(correct) = 1/4
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P(x = 15) = 48C15*(1/4)^15*(3/4)^33
= binompdf(48,1/4,15) = 0.0767
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Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The probability of successes in trials where is the probability of success on any given trial is given by:

Where is the number of combinations of things taken at a time and is calculated by

Plug in , , and and do the indicated arithmetic.

John

My calculator said it, I believe it, that settles it