Question 598375
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 probablility that the student will be able to answer 
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(a) all 10 of the questions on the exam, 
# of ways to succeed: 15C10 = 3003
# of possible outcomes: 20C10 = 184756
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P(10 correct) = 3003/184756 = 0.016
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(b) exactly 8 questions on the exam, and 
# of ways to succeed: 15C8*5C2  = 6435*10 = 64350
# of possible outcomes: 184756
P(8 correct) = 64350/184756 = 0.0348 
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(c) at least 9 questions on the exam. 
the answers were
[15C9*5C1 + 15C10]/20C10 = 0.152 
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Cheers,
Stan H.