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# 2.13 - G)P G = 0.7 × 0.6 1 × 0.6 – 0.7 × 1 × 0.6 0.7...

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2.13 (a) C = [(L M) G]] [(LM) G ] (b) Since (L M)G is contained in G, it is mutually exclusive to (LM) G which is contained in G . Hence P(C) is simply the sum of two terms, P(C) = P[(L M) G]] + P[(L M) G ] = P(LG MG) + P(L)P(M G ) = P(LG) + P(MG) – P(LMG) + P(L)P(M| G )P( G ) = P(L)P(G) + P(M|G)P(G) – P(L)P(M|G)P(G)+ P(L)P(M| G )P( G )
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Unformatted text preview: G )P( G ) = 0.7 × 0.6 + 1 × 0.6 – 0.7 × 1 × 0.6 + 0.7 × 0.5 × 0.4 = 0.74 (c) P( L|C) = P( LC)/P(C) = P( L{[(L ∪ M) G]} ∪ [(LM) G ])) / P(C) = P[ L (L ∪ M) G]] / P(C) since ( LL)M G is an impossible event = P( LMG) / P(C) = P( L)P(MG) / P(C) = P( L)P(M|G)P(G) / P(C) = 0.3 × 1 × 0.6 / 0.74 ≅ 0.243...
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