Your company sends out bids on a variety of projects. Some (actually 30% of all bids) involve a lot of work in preparing bids for projects you are likely to win, while the others are quick calculations sent in even though you feel it is unlikely that your company will win. Given that you put a lot of work into the bid, there is an 80% chance you will win the contract to do the project. Given that you submit a quick calculation, the conditional probability is only 10% that you will win.
a. Draw a probability tree for this situation.
b. What is the probability that you will win a contract?
c. Given that you win a contract, what is the conditional probability that you put a lot of work into the bid?
d. Given that you do not win a contract, what is the conditional probability that you put a lot of work into the bid?