Exercise 2.7.22. Let (1, F1, P1) be Lebesgue measure on [0, 1]. Con- sider a second probability triple, (92, F2, P2), defined as follows: 12 = {1, 2}, F2 consists of all subsets of $2, and P2 is defined by P2 (1} = P2{2} = =, and additivety. Let (0, F, P) be the product measure of (31, F1, P1) and (92, F2, P2). (a) Express each of 2, F, and P as explicitly as possible. (b) Find a set A E F such that P(A) =