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midterm1s - Math 425(Fall 07 Solutions for Midterm 1...

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Math 425 (Fall ’07) Solutions for Midterm 1 October 3, 2007 1 (20 pts) An instructor gives his class a set of 10 problems with the information that the midterm will consist of a random selection of 5 of them. If a student has figured out how to do 7 of the problems, what is the probability that he or she will answer correctly a) all 5 problems; b) at least 4 of the problems? Solution: a) ( 7 5 ) ( 10 5 ) b) P (at least 4 correct) = P (exactly 4 correct) + P (exactly 5 correct) P (at least 4 correct) = ( 7 5 ) + ( 7 4 ) · ( 3 1 ) ( 10 5 )
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2 (20 pts) A recent college graduate is planning to take the first three actuarial examinations in the coming summer. She will take the first actuarial exam in June. If she passes that exam, then she will take the second exam in July, and if she also passes that one, then she will take the third exam in September. If she fails an exam, then she is not allowed to take any others. The probability that she passes the first exam in 0.5. Given that she takes the second exam, the probability of passing the second exam is 0.9. Finally, assuming that she will take the September exam, she will pass the exam with probability 0.8.
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