SOLUTION: a consulting firm has submitted a bid for a large research project . The firm's management initially felt that there was a 50-50 chance of getting the bid . However , the agency to

Question 1176518: a consulting firm has submitted a bid for a large research project . The firm's management initially felt that there was a 50-50 chance of getting the bid . However , the agency to which the bid was submitted has subsequently requested additional information on the bid . Past experience indicates that on 75 % of the successful bids and 40 % of the unsuccessful bids additional information is requested ( a ) What is the probability that the bid will be successful ? ( ( b ) What is the conditional probability of a request for additional information , given that the bid will ultimately be successful ? (c)What is the probability that the agency will ask for the additional information ?( d ) Compute the probability that the bid will be successful given that a request for additional information has been received ?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's solve this problem using Bayes' Theorem.
**Define Events:**
* S: The bid is successful.
* U: The bid is unsuccessful.
* R: Additional information is requested.
**Given Probabilities:**
* P(S) = 0.50 (Initial probability of success)
* P(U) = 0.50 (Initial probability of failure)
* P(R|S) = 0.75 (Probability of request given success)
* P(R|U) = 0.40 (Probability of request given failure)
**(a) What is the probability that the bid will be successful?**
This is simply the initial given probability:
* P(S) = 0.50
**(b) What is the conditional probability of a request for additional information, given that the bid will ultimately be successful?**
This is directly given:
* P(R|S) = 0.75
**(c) What is the probability that the agency will ask for the additional information?**
We need to use the law of total probability:
* P(R) = P(R|S) * P(S) + P(R|U) * P(U)
* P(R) = (0.75 * 0.50) + (0.40 * 0.50)
* P(R) = 0.375 + 0.20
* P(R) = 0.575
**(d) Compute the probability that the bid will be successful given that a request for additional information has been received?**
We need to use Bayes' Theorem:
* P(S|R) = [P(R|S) * P(S)] / P(R)
* P(S|R) = (0.75 * 0.50) / 0.575
* P(S|R) = 0.375 / 0.575
* P(S|R) ≈ 0.6522
**Answers:**
* **(a) P(S) = 0.50**
* **(b) P(R|S) = 0.75**
* **(c) P(R) = 0.575**
* **(d) P(S|R) ≈ 0.6522**

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