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.

What is the prior probability that the bid will be successful (i.e., prior to receiving the request for additional information)?

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

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