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 75% of the successful bids and 44% of the unsuccessful bids the agency requested additional information.

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

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

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

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 75% of the successful bids and 44% of the unsuccessful bids the agency requested additional information.

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

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

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

Explanation / Answer

Let S1 denote the event of successfully obtaining the project.
S2 is the event of not obtaining the project.
B is the event of being asked for additional information about a bid.

a)
P(S1) = .5

b)
P(B|S1) = 0.75 (as it states in the problem)
c)

Use Bayes’ theorem to compute the posterior probability that a request for information indicates a successful bid.

P(S1|B) = P(S1 intersection B) / P(S1 intersection B) + P(S2 intersection B)

= (0.75 x 0.5)/((0.75 x 0.5) + (0.44 x 0.5))
= 0.63

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