Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 32% of all homeowners are insured against earthquake damage. Four homeowners are to be 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 that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.32)(0.68)(0.32)(0.32) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.)
x 0 1 2 3 4
p(x) ___ __ __ __ __

(c) What is the most likely value for X?
(d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)