Question

A consulting firm submitted a bid for a large research project. The firm’s management

Answer 1

Answer:

(a) 0.50

(b) 0.75

(c) 0.6522

Step-by-step explanation:

We are given that the firm’s management  initially had a 50–50 chance of getting the project.

Let Probability of getting a project or bid being successful, P(S) = 0.50

Probability of not getting a project or bid being unsuccessful, P(US) = 1 - 0.50 = 0.50

Also, Past  experience indicates that for 75% of the successful bids and 40% of the unsuccessful bids  the agency requested additional information which means;

Let event R = agency requested additional information

So, Probability that the agency requested additional information given the bid was successful, P(R/S) = 0.75

Probability that the agency requested additional information given the bid was unsuccessful, P(R/US) = 0.40

(a) Prior probability of the bid being successful = Probability of getting a project or bid being successful = $\frac{50}{100}$ = 0.50

(b) The conditional probability of a request for additional information given that  the bid will ultimately be successful = P(R/S) = 0.75

(c) The posterior probability that the bid will be successful given a request for  additional information is given by P(S/R) ;

Using Bayes' Theorem for this we get;

   P(S/R) = $\frac{P(S) * P(R/S)}{P(S)*P(R/S) + P(US) * P(R/US)}$ = $\frac{0.50 * 0.75}{0.50*0.75 + 0.50*0.40}$ = 0.6522 .