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 70% of the successful bids and 40% 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)?

Correct: Your answer is correct.

(b)

What is the conditional probability of a request for additional information given that the bid will ultimately be successful?

Correct: Your answer is correct.

(c)

Compute the posterior probability that the bid will be successful given a request for additional information. (Round your answer to two decimal places.)

Incorrect: Your answer is incorrect.

Answer 1

a) Prior probability of the bid being successful = 0.50

b) Conditional probability of a request for additional information given that the bid will ultimately be successful = P(request for additional information | bid will ultimately be successful)

= 0.70

c) Bayes' Theorem: P(A | B) = P(A & B) / P(B)

Probability that the bid will be successful given a request for additional information = P(bid will be successful | request for additional information)

= P(bid will be successful and request for additional information) / P(request for additional information)

= (0.5x0.70)/(0.5x0.70 + 0.5x0.40)

= 0.64

=