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Unformatted text preview: MAT 205 SPECIAL ASSIGNMENT #2 Part I 1 ) If two events, A and B , are such that P ( A ) = . 4, P ( B ) = . 8, and P ( ¯ A ∩ B ) = 0 . 5. (a) Find P ( A ∩ B ) (b) Find P ( A  B ) (c) Find P ( A ∩ B  A ∪ B ) (d) Determine if A and B are independent. Show your work. (e) Determine if A and B are mutually exclusive. Show your work. 2 ) If A and B are independent events with P ( A ) = 0 . 5 and P ( B ) = 0 . 2, find the following: (a) P ( A ∪ B ) (b) P ( ¯ A ∩ B ) (c) P ( ¯ A ∪ B ) (d) P ( ¯ A  B ) (e) P ( A  ¯ B ) 3 ) From a box with 40 red balls, 40 green balls and 20 blue balls, pick 6 balls one at a time at random and without replacement. Find the following probabilities: (a) P (red on 1st, 3rd and last while the remaining balls not red) (b) P (3 red) 4 ) Roll two dice and let x = (largest  smallest) of numbers on the two dice and define the events A = { x is even } , B = { x is odd } , and C = { x is less than 3 } . (a) Determine if A and B are mutually exclusive. (b) Determine if A and B are independent. (c) Find P ( A  B ) (d) Find P ( A  C ) 1 2 MAT 205 SPECIAL ASSIGNMENT #2 5 ) An advertising agency notes that approximately 1 in 50 potential buyers of a product sees a given magazine ad and 1 in 5 sees a corresponding ad on television. One in 100 sees both. One in 3 actually purchases the product after seeing the ad, 1 in 10 without seeing it. What is the probability that a randomly selected potential customer will purchase the product? 6 ) In a given region the probability of finding oil is 0.1. A test is often used to test for oil prior to drilling. From past experience it is known that when there is oil the test reads positive 95% of the time and when there is not oil the test reads negative 80% of the time. If you perform the test and it reads positive, what is the probability that there is oil....
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 Fall '10
 Any
 Statistics, Probability, Special assignment

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