A consulting firm submitted a bid for a large research project. The firm\'s mana

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 70% of the successful bids and 42% of the unsuccessful bids the agency requested additional information.

What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)?

What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)?

Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).

Explanation / Answer

Ans:

1)S=successful

US=unsuccessful

R=request information

Given that

P(S) = 0.5

P(R|S) = 0.70

P(R/US)=0.42

1)P(S)=0.5

2)P(R/S)=0.70

3)P(S|R) = P(S and R) / P(R )

= 0.5*0.70 / (0.5*0.70+ 0.5 * 0.42)

=0.35/(0.35+0.21)

= 0.35/0.56

=0.625

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