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Midterm1_solutions - STAT 230 Introduction to Probability...

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STAT 230: Introduction to Probability and Random Variables Summer 2009 Solutions for Midterm 1 Exercise 1 ( 20pts. ) A large group of people is to be checked for two common symptoms of a cer- tain disease. It is known that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess both symptoms, and the remainder pos- sess no symptoms. A person is chosen at random from the group. (a)-Find the probability that the person has neither symptom. ( 5pts. ) P ( A 0 B 0 ) = 1 - P ( A 0 B ) + P ( A B 0 ) + P ( A B ) = 1 - 0 . 3 + 0 . 2 + 0 . 1 = 0 . 4 (b)-Find the probability that the person has at least one symptom. ( 5pts. ) P ( A B ) = 1 - P ( A 0 B 0 ) = 1 - 0 . 4 = 0 . 6 (c)-Find the probability that the person has exactly one symptom. ( 5pts. ) P ( A B 0 ) + P ( A 0 B ) = 0 . 2 + 0 . 3 = 0 . 5 (d)-Find the conditional probability that the person has symptom A given that he has symptom B. ( 5pts. ) P ( A | B ) = P ( A B ) P ( B ) = P ( A B ) P ( B A )+ P ( B A 0 ) = 0 . 1 0 . 1+0 . 3 = 0 . 25 Exercise 2 ( 20pts. ) A box contains 100 computer chips, of which exactly 5 are good and the re- maining 95 are bad. The following three questions are independent of each other.
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