To find the prior probability, conditional probability and posterior probability.

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 than 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)?

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

c. Compute the posterior probability that the bid will be successful given a request for additional information.