{exercise 4.41 (algorithmic)} 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 80% of the successful bids and 37% of the unsuccessful bids the agency requested additional information. what is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)? what is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)? compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).