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 BAP A()()while it is clear from the following Venn diagram that P BA()= P(B) - P(AB). AABBAHence P BAP A(())= P BP ABP 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,
This is the end of the preview.
access the rest of the document.