1. In a large shipment of automobile tires, 10% have a flaw. Four tires are chosen at random to be installed on a car.
a. What is the probability that none of the tires have a flaw?
b. What is the probability that exactly one of the tires has a flaw?
c. What is the probability that one or more of the tires has a flaw?
2. Of the bolts manufactured for a certain application, 85% meet the length specification and can be used immediately, 10% are too long and can be used after being cut, and 5% are too short and must be scrapped.
a. Find the probability that a randomly selected bolt can be used (either immediately or after being cut).
b. Find the probability that fewer than 9 out of a sam- ple of 10 bolts can be used (either immediately or after being cut).