Problem $2-21($Algorithmic$)$

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 $65\%$ of the successful bids and $40\%$ of the unsuccessful bids the agency requested additional information. If required, round your answers to two decimal places.

a$.$ What is the prior probability that the bid will be successful $($i$.$e$.,$ prior to receiving 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 a posterior probability that the bid will be successful given that a request for additional information has been received.