Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let denote the number among the four who have earthquake insurance. 1. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and one who does not. Then one possible outcome is SFSS, with probability (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes].
2. What is the most likely value for X?
3. What is the probability that at least two of the four selected have earthquake insurance?