Suppose that 20% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance.
a. Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.2)(.8)(.2)(.2) and associated x value of 3. There are 15 other outcomes.)
b. What is the most likely value of x?
c. What is the probability that at least two of the four selected homeowners have earthquake insurance?