Question 586436: There were 20 multiple choice questions, each of which had only one correct answer from 4 choices. Assuming that she guesses on all 20 questions what is the probability that:
A. Get all 20 right?
B. Get exactly 14 questions (70%) right?
C. Get at least 12 questions right?
D. Get at least 14 questions right?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There were 20 multiple choice questions, each of which had only one correct answer from 4 choices.
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Binomial Problem with n = 20 ; p(correct) = 1/4 ; p(wrong) = 3/4
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Assuming that she guesses on all 20 questions what is the probability that:
A. Get all 20 right?
P(x = 20) = (1/4)^20 = 9.1x10^-13
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B. Get exactly 14 questions (70%) right?
P(x = 14) = 20C14*(1/4)^14*(3/4)^6 = binompdf(20,0.25,14) = 0.0000257
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C. Get at least 12 questions right?
P(12<= x <=20) = 1 - binomcdf(20,0.25,11) = 0.0009354
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D. Get at least 14 questions right?
P(14<= x <=20) = 1 - binomcdf(20,0.25,13) = 0.00002951
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Cheers,
Stan H.
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