Question

Nasee construction Co. is analyzing the probability of a bidding for the construction of. a new building. In the past, Nasee's main competitor, Nana construction Co. has submitted bids 90% of the time. if NANA bids on a project, the probability that NASEE will get the project is 10%. However, if NANA does not bid on a project, NASEE's probability of getting the project increases to 70%. if NASEE gets the project, what is the probability that NANA did not bid.?

Answer 1

Let A be the event that NANA Constructions bids for the project

Let B be the event that NANA Constructions did not bid for the project

Let X be the event that NASEE Constructions gets the project

Now,

Probability of event A happening, P(A) = 90% = 0.9

Probability of event B happening, P(B) = 1 – 0.9 = 0.1

Probability of NASEE Constructions getting the project when NANA Constructions bid for the project, P(X | A) = 10% = 0.1

Probability of NASEE Constructions getting the project when NANA Constructions does not bid for the project, P(X | B) = 70% = 0.7

To find Probability that NANA Constructions did not bid given that NASEE Constructions getting the project,

P(B | X) = [P(B) x P(X | B)] / [{P(A) x P(X | A)} + { P(B) x P(X | B)}] {By Baye's Theorem,}

                             = (0.1 x 0.7) / [(0.9 x 0.1) + (0.1 x 0.7)] = 0.4375