Question 114795: A student takes a quiz consisting of 5 multiple choice questions. Each question has 4 possible answers. If a student is guessing the answers at random, and the answers to different questions are independent,
A. Find the probability of giving 5 correct answers.
B. Find the probability of giving 5 incorrect answers.
C. Find the probability of giving at least 1 correct answer.
D. Find the probability of giving exactly 1 correct answer.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A student takes a quiz consisting of 5 multiple choice questions. Each question has 4 possible answers. If a student is guessing the answers at random, and the answers to different questions are independent,
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Four possible answers means P(correct answer) = 1/4; P(wrong answer) = 3/4
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Let "x" be the number of correct answers.
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A. Find the probability of giving 5 correct answers.
P(x=5) = (1/4)^5 = 0.000976...
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B. Find the probability of giving 5 incorrect answers.
P(x=0) = (3/4)^5 = 0.237...
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C. Find the probability of giving at least 1 correct answer.
P(x>=1)= 1 - P(x=0)
= 1 - 0.237...
= 0.76269....
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D. Find the probability of giving exactly 1 correct answer.
P(x=1) = 5C1(1/4)(3/4)^4 = 5*(1/4)(0.3164...) = 0.39550....
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Cheers,
Stan H.
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