Some parts of california are particularly earthquake-prone. suppose that in one metropolitan area, 25% 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 who has insurance and f one who does not. then one possible outcome is sfss, with probability (.) and associated x value 3. there are 15 other outcomes.] b. draw the corresponding probability histogram. 20. three couples and two single individuals have been invited to an investment seminar and have agreed to attend. suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). assume that different couples and individuals are on time or late independently of one another. let x 5 the number of people who arrive late for the seminar. a. determine the probability mass function of x. [hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] b. obtain the cumulative distribution function of x, and use it to calculate p(2 # x # 6) . 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?