You have just put in a bid for a large communications network. According to your best information you figure there is a 35% chance that your competitors will outbid you. If they do outbid you, you figure you still have a 10% chance of getting the contract by successfully suing them. However, if you outbid them, there is a 5% chance you will lose the contract as a result of their suing you.
a. Complete a probability tree for this situation.
b. Find the probability that you will be awarded the contract.
c. Find the probability that you will outbid your competitors and be awarded the contract.
d. Find the conditional probability that you will outbid your competitors given that you are awarded the contract.
e. Are the events "you were not awarded the contract" and "you outbid the competition" mutually exclusive? Why or why not?