Question 1176518
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**