Question

A consulting firm submitted a bid for a large research project. The firm's management initially felt there was a 50/50 chance of getting the bid. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Experience indicates that on 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information. If required, round your answers to two decimal places.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

Answer:

1. 0.50

2. 0.75

3. 0.65

Explanation:

1. For the bid being successful with a 50-50 chance, we have the probability:

50/(50 + 50) = 50 / 100 = 0.50

2. Given the request for additional info:

Probability = probability of request and successful / probability of successful

= 75 / 100 = 0.75

3. We will evaluate the probability of being successful given its request

We will use the Bayesian theorem

= [P(request | successful) * P(successful)] / [P(request | successful) * P(successful) + P(request | unsuccessful) * P(unsuccessful)]

= ( 0.75 * 0.5) / (0.75 * 0.5 + 0.4 * 0.5)

= 0.65