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practice1solutions

# practice1solutions - Statistics 400 Exam 1 Practice...

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Unformatted text preview: Statistics 400 Exam 1 Practice Problems 1. If P ( A ) = 0 . 3, P ( B ) = 0 . 8, and P ( A ∩ B ) = 0 . 1, find (a) P ( A ∪ B ), P ( A ∪ B ) = P ( A ) + P ( B )- P ( A ∩ B ) = 1 (b) P ( A ∩ B ), P ( A ∩ B ) = P ( B )- P ( A ∩ B ) = 0 . 7 (c) P ( A ∪ B ). P ( A ∪ B ) = P (( A ∩ B ) ) = 1- P ( A ∩ B ) = 0 . 9 (d) Are A and B independent? Why? No, because P ( A ∩ B ) 6 = P ( A ) P ( B ). 1 2. Among women who submit to a pregnancy test, Sixty-five percent (65%) are actually pregnant. A certain pregnancy test gives a false positive result with probability 0.02 and a valid positive result with probability 0.99. In other words, if a woman is pregnant, she gives a positive test result with probability 0.99. If a woman is not pregnant, she gives a positive test result with probability 0.02. (a) Among women who submit to a pregnancy test, what fraction of the tests are positive? Let T =”test positive” and A =”actually pregnant.” Then P ( A ) = 0 . 65, P ( T | A ) = 0 . 99, P ( T | A ) = 0 . 02....
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practice1solutions - Statistics 400 Exam 1 Practice...

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