Question

Two companies, a, b, supply readymade concrete to a large construction project. Each company has the capacity to provide the average concrete requirement for the project. However, during peak hours of a day, the capacities of both companies are needed, otherwise there will be setbacks in other parts of the project. Denote the following events: A = failure of company a to supply concrete; B = failure of company b to supply concrete. Data from previous projects show that P(A) = 0.05, P(B) = 0.07, P(AB) = 0.01. (a) If one of the two companies fail to deliver on a given day, what is the probability of failure of the other company on the same day? (b) What is the probability of no concrete delivery for the project on a given day? (c) If there is no concrete delivery during the peak hours of a day, what is the probability that it was caused by company a?

Answer 1

here P(A u B) =P(A)+P(B)-P(AB) =0.05+0.07-0.01=0.11

a)

P( If one of the two companies fail to deliver on a given day, what is the probability of failure of the other company on the same day)=P(A n B|AUB) =P(A n B)/P(A u B) =0.01/0.11=0.0909

b)

probability of no concrete delivery for the project on a given day =1-P(A u B) =1-0.11 =0.89

c)

If there is no concrete delivery during the peak hours of a day, what is the probability that it was caused by company a

=P(P(A)-P(A n B))/P(AuB) =(0.05-0.01)/0.11 =0.04/0.11=0.3636