Reference no: EM132851935

A consulting firm has submitted a bid for a large research project. The firm's management initially felt there was a 50-50 chance to getting the project. However, the agency to which the bid was submitted has subsequently re- quested additional information on the bid. Past experience indicates that on 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information.

(a) Draw a probability tree where the first stage represents whether the bid ultimately succeed or fail and where the second stage represents whether or not additional information will be requested.

(b) Flip the probability tree from part (a).

(c) What is the prior probability of the bid being successful (that is, prior to the request for additional information)?

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

(e) Use Bayes' Rule to compute a conditional probability that the bid will be successful given that a request for additional information has been received.

(f) Are the events "successful bid" and "additional information requested" independent? Show how you know this.