the smaller contract. The company estimates there is a 30% chance it will get the larger contract and a 60% chance it will get the smaller contract. Assuming the contracts will be awarded independently, what’s the expected profit? (Hint: create a probability model)4. A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races its value will jump to $100,000. If it wins one of the races, it will be worth $50,000. If it loses both races, it will be worth only $10,000. The man believes there’s a 20% chance that the horse will win the first race and a 30% chance it will win the second one. Assuming that the two races are independent events, find the man’s expected profit. (Hint: create a probability model)5. A consumer organization that evaluates new automobiles customarily reports the number of major defects on each car examined. Let X denote the number of major defects on a randomly selected car of a certain type. A large number of automobiles were evaluated, and a probability distribution consistent with these observations is X012345678910P(X).041.010.329.223.178.114.061.028.011.004a. Find the probability that the number of defects is at least 2.b. Find the expected number of defects. c. Find the standard deviation of the number of defects. c. Find the probability that X is within one standard deviation of the mean.