The percent of licensed U.S. drivers (from a recent year) that are female is 48.

Question

The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 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. male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

Construct a table and a tree diagram of the situation.

Find P(driver is female).

Find P(driver is age 65 or over|driver is female).

Find P(driver is age 65 or over AND female).

In words, explain the difference between the probabilities in part c and part d.

Find P(driver is age 65 or over).

Are being age 65 or over and being female mutually exclusive events? How do you know?

Explanation / Answer

Solution

(a) P(driver is female) = 0.4860

(b) P(driver is age 65 or over|driver is female) = P(driver over 65 and female)/P(female)

= (0.1361*0.4860)/0.486 = 0.1361

(c)  P(driver is age 65 or over AND female) = 0.1361*0.486 = 0.0661

(d) P(driver is age 65 or over) = 0.486*0.1361+0.1353*(1-0.486) = 0.1357

(e) No

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