Question

Suppose the percent of licensed U.S. drivers (from a recent year) that are female is 49.50. Of the females, 5.19% are age 19 and under; 79.24% are age 20-64; 15.57% are age 65 or over. Of the licensed U.S. male drivers, 5.25% are age 19 and under; 79.32% are age 20-64; 15.43% are age 65 or over.

a. construct a contingency table of the situation( round to two decimal places)

	19 and under	20-64	65 and over	Total
Female	%	%	%	%
Male	%	%	%	%
Total	%	%	%	100%

b. P(driver is female)

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

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

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

f. P(driver is age 65 or over) g. Are being age 65 or over and being female mutually exclusive events? How do you know?

Answer 1

(a) The contingency table is given below.

	19 and under	20-64	65 or over	Total
Female	2.57%	39.22%	7.71%	49.50%
Male	2.65%	40.06%	7.79%	50.50%
Total	5.22%	79.28%	15.50%	100.00%

(b) P(driver is female) = 49.50% = 0.4950.
(c) P(driver is age 65 or over | driver is female) = P(driver is age 65 or over and driver is female)/P(driver is female) = 7.71%/49.50% = 0.1557.
(d) P(driver is age 65 or over AND female) = 0.0771.
(e) In parts (c) and (d), there are 2 events; A = driver is age 65 or over and B = driver is female. In part (c), we are calculating the probability P(A | B), a conditional probability. In part (d), we are calculating the probability P(A B), an inter-sectional probability.
(f) P(driver is age 65 or over) = 0.1550.
(g) Here, being age 65 or over and being female are not mutually exclusive events, because P(65 or over and female) is not equal to 0. It is equal to 0.0771.