A consulting firm submitted a bid for a large research project. The firm\'s mana

Question

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information. What is the prior probability of the bid being successful (that is, prior to the request for additional information)? What is the conditional probability of a request for additional information given that the bid will ultimately be successful? Compute the posterior probability that the bid will be successful given a request for additional information.

Explanation / Answer

Solution

Back-up Theory

Conditional Probability of B given A, P(B/A) = P(BA)/P(A) ……………………(1)

P(B) = {P(B/A) x P(A)} + {P(B/Ac) x P(Ac)} …....…………………………………..(2)

P(A/B) = {P(B/A) x P(A)}/P(B) ………………….............................................…(3)

Now, to work out the solution,

Let A be the event that the bid for the project is successful and B the event that the agency requests for additional information.

Part (a)

Given, the consulting firm initially felt they had 50:50 chance of getting the project

=> prior probability of bid being successful = P(A) = ½. ANSWER

Part (b)

Conditional probability of request for additional information given that the bid will be ultimately successful = P(B/A) = 0.75 ANSWER [because given that “for 75% of successful bids and 40% of unsuccessful bids, the agency requests for additional information”]

Part (c)

Posterior probability the bid will be successful given that additional information had been requestd

= P(A/B) = {P(B/A) x P(A)}/P(B) [vide (3) under Back-up Theory]

Now, given that “for 75% of successful bids and 40% of unsuccessful bids, the agency requests for additional information” => P(B/A) = 0.75 and P(B/Ac) = 0.40.

Also, by (3) under Back-up Theory, P(B) = {(0.75 x 0.5) + (0.40)(0.5)} = 0.575.

So, P(A/B) = 0.75 x (0.5/0.575) = 0.652 ANSWER

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