Question

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 72% of the successful bids and 39% of the unsuccessful bids the agency requested additional information.

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

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

c. Compute the posterior probability that the bid will be successful given a request for additional information (to  decimals).

Answer 1

let A be the event of suceessfully obatining project and B is the event of not obtaing project
also C is the event asked for additional nformation about a bid
a.P(A)=0.5 (prior request to additional information)

b.P(C|A)=0.72 (conditional prob. of a request for additional information given that bid will ultimately be successful )

c.by using Bayes theorem to calculate posterior probability that the bid will be sucessful given for additional information.

$P(C|A)=\frac{P(A\bigcap C)}{P(A\bigcap C)+P(B\bigcap C)}$

$=\frac{0.5*0.72}{(0.5*0.72)+(0.5*0.39)}$

$=\frac{0.36}{(0.36)+(0.195)}$

  $=\frac{0.36}{(0.555)}$

  $=0.649$

==0.65