SOLUTION: An instructor assigns 10 problems and says that the final exam will consist of a random selection of 5 of them. If a student knows how to solve 7 of the problems, what is the proba

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Question 1198934: An instructor assigns 10 problems and says that the final exam will consist of a random selection of 5 of them. If a student knows how to solve 7 of the problems, what is the probability that he or she will answer correctly
a) all 5 problems
b)at least 4 problems

Answer by ikleyn(52803) About Me  (Show Source):
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An instructor assigns 10 problems and says that the final exam will consist
of a random selection of 5 of them. If a student knows how to solve 7 of the problems,
what is the probability that he or she will answer correctly
a) all 5 problems
b)at least 4 problems
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(a)  P = C%5B7%5D%5E5%2FC%5B10%5D%5E5 = 21%2F252 = reduce = 1%2F12.    ANSWER


     The denominator is the number of all possible quintuples of 10 problems.

     The numerator is the number of all possible quintuples of 7 known problems.



(b)  P = %28C%5B7%5D%5E4%2AC%5B3%5D%5E1+%2B+C%5B7%5D%5E5%29%2FC%5B10%5D%5E5 = %2835%2A3%2B21%29%2F252 = 126%2F252 = reduce = 1%2F2.    ANSWER


     The denominator is the number of all possible quintuples of 10 problems.

     The numerator is the number of all possible quintuples containing 4 or 5 known problems.

Solved, with full explanations.