Answer:
P(S/A) = 0.6235
Step-by-step explanation:
Let's call S that you successfully bid, S' that you unsuccessfully bid, A that the agency asked for more information and A' that the agency didn't asked for more information.
So, the probability P(S/A) that the bid is successful given that the agency asks for more information is calculated as:
P(S/A) = P(S∩A)/P(A)
Where P(A) = P(S∩A) + P(S'∩A)
Then, the probability P(S∩A) that you successfully bid and the agency asked for more information is:
P(S∩A) = 0.51 * 0.7 = 0.357
Because your firm has a 51% of successfully landing the contract and if you successfully bid, then the probability the agency asks for information is 70%.
At the same way, the the probability P(S'∩A) that you unsuccessfully bid and the agency asked for more information is:
P(S'∩A) = (1-0.51) * 0.44 = 0.2156
So, P(A) and P(S/A) are equal to:
P(A) = 0.357 + 0.2156 = 0.5726
P(S/A) = 0.357/0.5726 = 0.6235
