Baye's Theorem, find conditional probablity of...

Hi helpers,

I am currently taking a Statistic class and am on the Baye's Theorem section. I need to complete the following three questions, but I am troubled by one of them. Please kindly advise on how I can find the answer.

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 70% of the successful bids and 41% 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)?
--- I got .50.


b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful?
Would someone please help me on how to attack this problem?

c. Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals)?
--- Using the formula, I found the answer to be .625.

Thank you..!

Sometimes it is handy to make a chart. That way, one can answer most any "what is the probability.....given that...." type problem.

Assume an arbitrary 1,000 bids overall. It is an easy number to work with.

\(\displaystyle \begin{array}{c|c|c|c} \;\ &\text{successful}&\text{not successful}&\text{total} \\ \hline\text{add. info}&350&205&555 \\ \text{no add. info}&150&295&445\\ \text{total} &500&500&1000\end{array}\)

Now, suppose it asked, "what is the probability that a bid is successful given that there was no additional info asked for?".

Go down the successful column and across the no add. info row and we get \(\displaystyle \frac{150}{445}=\frac{30}{89}\approx .337\)

Nice explanation ... Cody