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. Historical record indicates that 75% of the successful bids the agency requested additional information, and 40% of the unsuccessful bids the agency requested additional information. What is the probability that the bid will be successful given a request for additional information

Answer 1

0.6522

Explanation:

From the given information:

The probability of success i.e P(Success) = The probability of failure i.e. P(failure)

∴

P(Success) = P(failure) = 50% = 0.50

The probability P(additional information | successful) = 75%

The probability P(additional information | unsuccessful) = 40%

Hence, the probability that the bid will be successful = 0.5

The probability that the additional info| successful = 0.75

The probability that the bid will be successful provided that there is a request for additional information can be determined by using the Naive Bayes Theorem.

`= (P(success) *P(additional \ info \ | \ success) )/(P(additional \ info))`

`= (0.5 * 0.75)/((0.50 * 0.75) +(0.50 * 0.4))`

`= (15)/(23)`

`\mathbf{= 0.6522}`