Contract bidding. As manager for a construction firm, you are in charge of bidding on two large contracts. You believe the probability you get contract #1 is 0.8. If you get contract #1, the probability you also get contract #2 will be 0.2, and if you do not get #1, the probability you get #2 will be 0.4.

a) Sketch the probability tree.

b) What is the probability you will get both contracts?

c) Your competitor hears that you got the second contract but hears nothing about the first contract. Given that you got the second contract, what is the probability that you also got the first contract?