3.5 Exercise 31

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are women is 48.60. Of the women, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of the licensed U.S. men drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

Complete the following.

1. Construct a table or a tree diagram of the situation.
2. Find P(driver is a woman).
3. Find P(driver is age 65 or over $\left|\right.$ driver is a woman).
4. Find P(driver is age 65 or over $\cap$ a woman).
5. In words, explain the difference between the probabilities in part c and part d.
6. Find P(driver is age 65 or over).
7. Are being age 65 or over and being a woman mutually exclusive events? How do you know?