11Ma2bHw1

11Ma2bHw1 - MATH 2B WINTER 2012 HOMEWORK 1 DUE MONDAY 1/9...

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MATH 2B WINTER 2012 HOMEWORK 1 DUE MONDAY 1/9 AT 10AM All numbered problems are from Pitman. 1.3.8: Let A and B be events such that P ( A ) = 0 . 6, P ( B ) = 0 . 4, P ( AB ) = 0 . 2. Find the probabilities of: (a) A B , b) A c , c) B c , d) A c B , e) A B c f) A c B c 1.3.13: Boole’s inequality. The inclusion-exclusion formula gives the proba- bility of a union of events in terms of probabilities of intersections of the various subcollections of these events. Because this expression is rather complicated, and probabilities of intersections may be unknown or hard to compute, it is useful to know that there are simple bounds. Use induction on n to derive Boole’s inequality : P ( S n i =1 A i ) n i =1 P ( A i ). 1.4.5: There are two urns. The ﬁrst urn contains 2 black balls and 3 white balls. The second urn contains 4 black balls and 3 white balls. An urn is chosen at random, and a ball is chosen form that urn. (a) Draw a suitable tree diagram. (b) Assign probabilities and conditional probabilities to the

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This note was uploaded on 03/21/2012 for the course MATH 2b taught by Professor Ericrains during the Winter '11 term at Caltech.

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11Ma2bHw1 - MATH 2B WINTER 2012 HOMEWORK 1 DUE MONDAY 1/9...

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