PROBLEM 2. (a) We toss a fair coin three times. Find the probability that exactly two heads occur, given that the first toss was a heads. (b) We roll a standard 6-sided die twice. Find the probability that the sum of the faces is greater than 7, given that the rst roll was less than 5. (c) We roll two standard 6-sided dice once. Find the probability that the sum of the two rolls is 6 given that the dice land on different numbers. (d) Let x be a point selected uniformly at random from the interval [0, 1]. Find the probability that x > 1/2, given that x2 x+2/9