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Unformatted text preview: Solutions to Homework 02 1. We are interested in the shaded region shown in Figure 1. The shaded are on the left corresponds to A B C while that on the right is A C B . Also, the unshaded area common to both A and B is A B . Now, note that A = ( A B C ) ( A B ) P [ A ] = P [ A B C ] + P [ A B ] P [ A B C ] = P [ A ] P [ A B ] similarly P [ A C B ] = P [ B ] P [ A B ] Then, P [( A B C ) ( A C B )] = P [ A B C ] + P [ A C B ] = P [ A ] P [ A B ] + P [ B ] P [ A B ] = P [ A ] + P [ B ] 2 P [ A B ] A B Figure 1: Venn diagram for question 1. 2. Refer to Figure 2(a) for the region A C B C . P [ A C B C ] = 1 P [ A B ] = 1 z 1 Refer to Figure 2(b) for the region A B C . P [ A B C ] = P [ A ] P [ A B ] = x z Refer to Figure 2(c) for the region A C B . P [ A C B ] = 1 P [ A B C ] = 1 ( x z ) = 1 x + z Refer to Figure 2(d) for the region A C B C ....
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 Spring '03
 WOODS

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