Living Arrangements. As reported by the U.S. Census Bureau in America’s Families and Living Arrangements, the living arrangements by age of U.S. citizens 15 years of age and older are as shown in the following joint probability distribution. Age (yr)

Living arrangement Alone With spouse With others L1 L2 L3 P(Ai)

15–24 0.006 0.012 0.157 0.175 A1 25–44 0.030 0.184 0.123 0.337 A2 45–64 0.047 0.216 0.067 0.330 A3 Over 64 0.046 0.088 0.024 0.158 A4 P(Lj) 0.129 0.500 0.371 1.000 A U.S. citizen 15 years of age or older is selected at random. Determine the probability that the person selected

a. lives with spouse.

b. is over 64.

c. lives with spouse and is over 64.

d. lives with spouse, given that the person is over 64.

e. is over 64, given that the person lives with spouse.

f. Interpret your answers in parts (a)–

(e) in terms of percentages.