A company is participating in a bidding for two government contracts. A manager of the company estimates that there is a 40% chance that the company will win the bidding for the first contract, a 30% chance for the second contract, and a 20%chance for the both contracts.

(a) What is the probability the company will win the bidding for the first contract only? For the second contract only?

(b) What is the probability the company will win the bidding for at least one contract?

2. To reduce theft, a company proposes to screen the workers with a lie-detector test that has been proved correct 90% of the time (for guilty subjects, and also for innocent subjects). The company will fire all the workers who fail the test. Suppose that 5% of workers steal from time to time.

(a) If a worker is fired, what is the conditional probability he is innocent?

(b) If a worker is not fired, what is the conditional probability he is guilty?

Include a probability tree for this problem.