Question

You work for a consulting firm, and have submitted a bid for a large consulting contract. The firm's management thinks it has a 50-50 chance of landing the project. In a few weeks, the agency to which the bid was submitted sent in a request for additional information. The firm's past experience indicates that the agency asked for additional information for 72.1% of successful bids and 14.5% of unsuccessful bids. What is the probability that this particular bid will be successful, given that the request for additional information happened? Enter answer in percents, accurate to two decimal places.

Answer 1

Using Bayes theorem, Probability = (0.5 x 72.1%) / (0.5 x 72.1% + 0.5 x 14.5%) = 0.8326 or 83.26%

Explanation : The probability of the first outcome, i.e., probability of landing the project without additional information is 0.5 for successful and 0.5 for unsuccessful. Now, probability of the second outcome, i.e., probability of landing the project with additional information asked for is 72.1% for successful and 14.5% for unsuccessful for each of the first outcome, i.e, (0.5 x 72.1%) out of total probablity of (0.5 x 72.1% + 0.5 x 14.5%) for successful bid and (0.5 x 14.5%) out of total probablity of (0.5 x 72.1% + 0.5 x 14.5%) for unsuccessful bid.