1. Color blindness is a gender-linked inherited condition that is much more common among men than women. Suppose that 8% of all men and .5% of all women are color-blind. A person is chosen at random and found to be color-blind. What is the probability that the person is male? (You may assume that 50% of the population are men and 50% are women.)
2. A factory has two machines that produce bolts. Machine I produces 60% of the daily output of bolts, and 3% of its bolts are defective. Machine II produces 40% of the daily output, and 2% of its bolts are defective.
(a) What is the probability that a bolt selected at random will be defective?
(b) If a bolt is selected at random and found to be defective, what is the probability that it was produced by machine I?