A consulting firm has submitted a bid for a large research p

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 requested
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.

Solution

(c) 0.75

(d) 0.60

(e) 0.45

(f) The events are independent because the added infornation is required for unsuccessful bid