solve these by using chapter 2 and 4 of book Probability and statistics for engineers and scientist Ninth edition

Q # 1 (a); Two boxes of the similar dimension are given as follows:Box A contains 5 green and 7 white balls.Box B contains 4 green and 3 white balls.A ball is selected at random and a ball is drawn from the box.1) What is the probability that the ball drawn is green?2) If the ball is green, what is the probability that it came from box A? (b); a shelf contains 4 shirts which are known to be either: i) all black or ii) two black and two blue. A shirt is randomly selected and it seems to be black. Find the probability of all black shirts in the shelf? Q # 2 (a) Let X and Y be independent random variables such that X = I prob. 1/3 prob. 2/3 Y = 1-3 2 prob. 3/4 prob. 1/4 Find (a) E(3X + 2Y). (b) E(2X2 - Y2), (c) E(XY). (d) E(XzY). (b) Let fix, y) = (=(2r+ y) Os xs1, 0sys2 . Find (a) E(X), (b) E(Y). (c) E(X?). (d) E(Y?). otherwise (e) E(X + Y). (f) E(XY)