1. Ultra Construction Company is bidding on three contracts. The probability of winning contracts A, B, and C are 0.35, 0.75, and 0.65, respectively. Find the probability that the company will win (a) all three contracts and (b) any two of the three contracts.
2. Vendors I, II, III, and IV provide all the fresh concrete that ABC Construction purchases. From these vendors, the firm purchase 25, 35, 10, and 30%, respectively, of the concrete it needs on a daily basis. It is known from past experience that vendors I, II, III, and IV provide 80, 95, 70, and 90% perfect concrete. What is the probability that a randomly selected concrete batch is not perfect? Given that a concrete batch is not perfect, what is the probability that it came from vendor III?