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 79% of the successful bids and 42% of the unsuccessful bids the agency requested additional information.

a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)?

b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)?

c. Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).

Answer 1

Suppose, the event of successful bid is denoted by S and the event of requesting additional information is denoted by A.

From the given information,

(a)

Prior probability of the bid being successful is given by P(S) = 0.5

(b)

Conditional probability of a request for additional information given that the bid will ultimately be successful is given by P(A|S) = 0.79

(c)

The posterior probability that the bid will be successful given a request for additional information is given by P(S|A) which is calculated as follows using Bayes' theorem.