41. A consulting firm submitted a bid for a large research project. The firm\'s

Question

41. 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 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)? What is the conditional probability of a request for additional information given that the bid will ultimately be successful? b. Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208 4 Introduction to Probability Compute the posterior probability that the bid will be successful given a request for additional information

Explanation / Answer

a) prior probability of bid being successful P( being successful)=0.5

b)condtional probability =P( information requested|being successful) =0.75

c) probability that additional information is requested =P(nformation requested)

=P(( being successful)*P( information requested|being successful) +P(( being unsuccessful)*P( information requested|being unsuccessful) =0.5*0.75+0.5*0.4=0.575

therefore probability of bid will be successful given request for additional information

=P(being successful) |information requested)

=P(( being successful)*P( information requested|being successful) /P( information requested)

=0.5*0.75/0.575=0.652174

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