Question 78387: A class is given a list of 20 study problems from which 10 will be chosen as part of an upcoming exam.A given student knows how to solve 15 of the problems.Find the probability that the student will be able to answer
a. all 10 questions on the exam
b. exactly 8 questions on the exam
c. at least 9 questions on the exam
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A class is given a list of 20 study problems from which 10 will be chosen as part of an upcoming exam.A given student knows how to solve 15 of the problems.Find the probability that the student will be able to answer
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Prob(he will know the answer on any one of the questions) = 15/20=3/4
a. all 10 questions on the exam
This is a binomial poblem with n=10, p=3/4, x=10
P(10 right) = (3/4)^10 = 0.056
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b. exactly 8 questions on the exam
P(8 right)= 10C8(3/4)^8(1/4)^2 = 0.281567...
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c. at least 9 questions on the exam
P(9 or 10) = 1- binomcdf(10,.75,8) = 0.244025...
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Cheers,
Stan H.
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