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 40% 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)?

b.What is the conditional probability of a request for additional information given that the bid will ultimately be successful?

c.Compute the posterior probability that the bid will be successful given a request for additional information

CAN YOU EXPLAIn THE SOLUTIONS IN DETAIL, IF YOU CAN, THANK YOU!!!! :)

Answer 1

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.

Hence, Probabilities of above-mentioned events may be given as

P(S₁) = 0.5

P(S₂) = 0.5

(A). The probability of the bid being successful,

P(S₁) = 0.5 (direct result from question)

(B). The conditional probability of a request for additional information given that the bid will ultimately be successful,

P(B | S₁) = .75 (direct result from question, definition of conditional probability)

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

Above formula is a direct interpretation of Bayes theorem. Also, probability of intersection of two events if found using the following formula

P(A ∩ B) = P(A) P(B|A)

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