Question

A consulting firm submitted a bid for a large research project. The firms 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 indicated that on 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information.

(a) What is the prior probability 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?

Answer 1

a) 0.5

b) 0.75

Explanation:

a) The prior probability of the bid being successful is 0.5, as stated in the question. 50/50 means half or 0.5 probability.

b) If it is already given that a bid will be successful, the probability a request for additional information is made is also stated within the question. When we state that the bid is guaranteed to be successful, we don't need to consider the 50/50 chance or the 40% unsuccessful bid requests. It is clearly stated that when a successful bid is made, there is a 75% chance the agency requests for additional information. Since that is already a given, the answer we're looking for here is 75% or 0.75 probability.