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2.10 - 2.10(a The event both subcontractors will be...

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2.10 (a) The event “both subcontractors will be available” = AB , hence since P ( A B ) = P ( A ) + P ( B ) - P ( AB ) P ( AB ) = P ( A ) + P ( B ) - P ( A B ) = 0.6 + 0.8 - 0.9 = 0.5 (b) P (B is available A is not available) = P ( B A ) = P BA P A ( ) ( ) while it is clear from the following Venn diagram that P BA ( ) = P ( B ) - P ( AB ). A AB B A Hence P BA P A ( ( ) ) = P B P AB P A ( ) ( ) ( ) 1 = (0.8 - 0.5)/(1 - 0.6) = 0.3/0.4 = 0.75 (c) (i) If A and B are s.i., we must have P(B A) = P(B) = 0.8. However, using Bayes’ rule,
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