he City of Columbia Missouri is upgrading the Columbia Regional Airport due to t

Question

he City of Columbia Missouri is upgrading the Columbia Regional Airport due to the growth in the number of passengers using the airport every year by adding a new terminal. Two different sites, Site A and Site B are candidates for the upgrading plan (See Figure 1 below). There is a 40% chance that Site A will be chosen for the new terminal while Site B has a probability of 60% to be selected for that purpose. If Site A was selected for the new terminal, the probability that the Airport will be able to provide its current services is 50% while if Site B is selected, the probability that the Airport will be closed is 10%. a) What is the probability that the Columbia Regional Airport will fail to provide its current service due to the construction of the new terminal? B) Given that the Airport failed to provide its services due to the construction of the new terminal, what is the probability that Site B was selected for the new terminal?

Explanation / Answer

probabilty of chossing site A =P(A)=0.4

and probabilty of choosing site B =P(B) =0.6

probabiliby of being failed to deliver =P(F)

probabilty of failed to deliver if site A is chosen=P(F|A) =1-0.50=0.5

probabilty of failed to deliver if site B is chosen =P(F|A) =0.1

a)probability that the Columbia Regional Airport will fail to provide its current service due to the construction of the new terminal =P(F) =P(A)*P(F|A)+P(B)*P(F|B) =0.4*0.5+0.6*0.1=0.26

b)Given that the Airport failed to provide its services due to the construction of the new terminal,probability that Site B was selected for the new terminal=P(B|F) =P(B)*P(F|B)/P(F) =0.6*0.1/0.26=0.230769

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