Your consulting firm is submitting a bid for a big contract. From previous data, you know your firm has a 51% of successfully landing the contract. The agency to which you submitted your bid has asked for more information about your bid. Past experience indicates that for 70% of successful bids and 44% of unsuccessful bids, the agency asks for more information. (In other words, if you successfully bid, then the probability the agency asks for information is 70%, etc.) If an agency asks for more information, what is the probability the bid is successful

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