Looking at the United States population in 1993 the probabil

Looking at the United States population in 1993, the probability of a working adult between the ages of 35 and 64 having health insurance coverage of any kind is 0.856.
a. A 42-year-old woman and an unrelated 60-year-old man are randomly selected from this population. What is the probability that both individuals are uninsured?

b. What is the probability that both adults have health insurance coverage?

c. If four unrelated adults between the ages of 40 and 60 are chosen from the population, what is the probability that all four are insured?

Solution

(a) Since these events are independent, the probability that both adults are uninsured is
P(both uninsured) = P(woman uninsured) × P(man uninsured)
= (1-0.856) × (1-0.856)
= 0.015.
(b) The probability that both adults are insured is
P(both insured) = 0.856 × 0.856
= 0.7327
(c) The probability that all 4 adults are uninsured is
(1-0.856)^4 = 0.0004299.