Example_class_2_slides

For example a1 a2 a3 are independent if and only if p

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Unformatted text preview: tually) independent if and only if the probability of the intersection of any combination of them is equal to the product of the probabilities of the corresponding single events. For example, A1 , A2 , A3 are independent if and only if P (A1 ∩ A2 ) = P (A1 )P (A2 ) P (A1 ∩ A3 ) = P (A1 )P (A3 ) P (A2 ∩ A3 ) = P (A2 )P (A3 ) Chan Chi Ho, Chan Tsz Hin & Shi Yun Example class 2 Problem 1 Problem 1 If P (A) = 0.5, P (B ) = 0.3, P (A ∩ B ) = 0.1, find 1 P (Ac ) 2 P (A ∪ B ) 3 P (A\B ) 4 P (Ac ∩ B c ) 5 P (Ac ∪ B c ) Chan Chi Ho, Chan Tsz Hin & Shi Yun Example class 2 Solution to Problem 1 Solution 1 P (Ac ) = 1 − 0.5 = 0.5 2 P (A ∪ B ) 4 5 P (A) + P (B ) − P (A ∩ B ) = 3 = 0.5 + 0.3 − 0.1 = 0.7 Note that P (A\B ) = P (A ∩ B c ), and P (A ∩ B ) + P (A ∩ B c ) = P (A) P (A ∩ B c ) = 0.5 − 0.1 = 0.4 By De Morgan’s Law, Ac ∩ B c = (A ∪ B )c P (Ac ∩ B c ) = 1 − P (A ∪ B ) = 1 − 0.7 = 0.3 By De Morgan’s Law, Ac ∪ B c = (A ∩ B )c P (Ac ∪ B c ) = 1 − P...
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This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

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