Call a household prosperous if its income exceeds $100,000. call the household educated if the householder completed college. select an american household at random, and let a be the event that the selected household is prosperous and b the event that it is educated. according to a survey, p(a) = 0.132, p(b) = 0.227, and the probability that a household is both prosperous and educated is p(a and b.= 0.082. what is the conditional probability that a household is prosperous, given that it is educated? (round your answer to four decimal places.) .3612 explain why your result shows that events a and b are not independent. if a and b were independent, then p(a|b) would equal p(a), and p(a and b. would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(a), and p(a and b. would equal the sum p(a) + p(b). if a and b were independent, then p(a|b) would equal p(a and b), and p(a and b. would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and b. would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and b. would equal the sum p(a) + p(b). submit answer save progress