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 79% of the successful bids and 42% 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 1
decimal)?

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

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

Answer #1

Suppose, the event of successful bid is denoted by S and the event of requesting additional information is denoted by A.

From the given information,

**(a)**

Prior probability of the bid being successful is given by
**P(S) = 0.5**

**(b)**

Conditional probability of a request for additional information
given that the bid will ultimately be successful is given by
**P(A|S) =
0.79**

**(c)**

The posterior probability that the bid will be successful given
a request for additional information is given by P(S|A) which is
calculated as follows using **Bayes' theorem**.

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The firm's management initially felt they had a 50-50 chance of
getting the project. However, the agency to which the bid was
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Past experience indicates that for 77% of the successful bids and
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