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Unformatted text preview: ( B  A ) = P ( A  B )(4 / 7) P ( A  B )(4 / 7) + P ( A  B c )(3 / 7) = 4 P ( A  B ) 4 P ( A  B ) + 3 P ( A  B c ) . To Fnd P ( A  B ) we realize that to get two dimes total, if one dime is from urn I, then only one can come from the other two urns. Therefore, we need to Fnd the probability of selecting only one dime from the two remaining urns. This is given by: P ( A  B ) = (2 / 7)(1 / 4) + (5 / 7)(3 / 4) = 17 / 28 . Similarly, we see P ( A  B c ) as the probability that we chose dimes from both of the other urns. Therefore P ( A  B ) = (5 / 7)(1 / 4) = 5 / 28 . Therefore, P ( B  A ) = 4 P ( A  B ) 4 P ( A  B ) + 3 P ( A  B c ) = 4 * (17 / 28) 4 * (17 / 28) + 3 * (5 / 28) = 4 * 17 4 * 17 + 3 * 5 = 68 83 = 0 . 819277 . 1...
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 Spring '08
 Anderson
 Math, Probability

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