Question 129661: Richard has just been given a ten-question multiple choice test in his history class. Each question has five answers only one of which is correct. Since Richard has not attended class recently, he does not know any of the answers. Assume that Richard guesses randomly on all ten questions.
a) Find the probability that he will answer all 10 questions correctly.
b) Find the probability that he will answer 5 or more questions correctly.
c) Find the probability that he will answer none of the questions correctly.
d) Find the probability that he will answer at least 3 questions correctly
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Probability-and-statistics/129661 (2008-02-28 15:53:10): Richard has just been given a ten-question multiple choice test in his history class. Each question has five answers only one of which is correct. Since Richard has not attended class recently, he does not know any of the answers. Assume that Richard guesses randomly on all ten questions.
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This is a binomial problem with:
P(answer is correct) = 1/5=0.2
P(answer is wrong) = 4/5
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Number of trials is 10
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a) Find the probability that he will answer all 10 questions correctly.
P(10,0.2,10) = (1/5)^10
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b) Find the probability that he will answer 5 or more questions correctly.
Ans: 1 - binomcdf(10,0.2,4) = 0.03279...
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c) Find the probability that he will answer none of the questions correctly.
Ans: (4/5)^10
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d) Find the probability that he will answer at least 3 questions correctly
Ans: 1-binomcdf(10,0.2,2) = 0.322200...
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Cheers,
Stan H.
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