Complete question is;
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 74% of the successful bids and 39% of the unsuccessful bids the agency requested additional information.
1. What is the prior probability of the bid being successful (that is, prior to the request for additional information)?
2. What is the conditional probability of a request for additional information given that the bid will ultimately be successful?
3. Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).
Answer:
1) 0.5
2)0.74
3) 0.65
Explanation:
1) Since we are told that they had a 50-50 chance of getting the project, Thus;
Probability of a successful bid is;
P(Successful bid) = 50/(50 + 50) = 50/100 = 0.5
2) We are told that for 74% of the successful bids, the agency requested additional information. Thus;probability of a request for additional information given that the bid will ultimately be successful is;
P(request|successful) = 74% = 0.74
3) For us to find the posterior probability that the bid will be successful given a request for additional information will be gotten using bayes theorem to get;
P(successful|request) = [P(request|successful) × P(Successful bid)] / [(P(request|successful) × P(Successful bid)) + (P(request|unsuccessful bid) × P(unsuccessful bid))]
P(request|unsuccessful bid) is given as 0.39 and P(unsuccessful) will be 0.5.
Thus;
P(successful|request) = (0.74 × 0.5)/[(0. 74 × 0.5) + (0.39 × 0.5)] ≈ 0.65