Question 137808: A student takes a 10 question multiple choice test (each with four options, A-D) without studying or attending class. He plans to guess. A score of 6 out of 10 is needed to pass, 8 out of 10 for high pass.
a. What are his chances of passing by guessing?
b. What are his chances of a high pass just by guessing?
c. Should he manage to pass, how likely would it be a high pass?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A student takes a 10 question multiple choice test (each with four options, A-D) without studying or attending class. He plans to guess.
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A score of 6 out of 10 is needed to pass,
8 out of 10 for high pass.
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It is a binomial problem with p = 1/4, n=10
a. chances of passing by guessing? P(x>=6) = 1-binomcdf(10,0.25,5)=0.01928
b. chances of a high pass just by guessing?= 1-binomcdf(10,0.25,7)=0.0004158..
c. Should he manage to pass, how likely would it be a high pass?
P(high pass| pass) = P(high pass AND Pass)/P(pass)=0.0004158/0.01928=0.02157
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Cheers,
Stan H.
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