1. Let X ~ N(0, 1) and Y ~ N(0, 3). Consider a game where you toss a fair coin, and if heads you win X dollars, and if tails you win Y dollars. (If you "win" a negative amount of money, you instead lose that much money - so if you flip tails and Y = -1.5, you lose $1.50). Suppose you will play this game one time. hint: If you're having trouble with part (b) or (c), a probability tree may help (a) Find the probability that you win at least $2 if you toss heads and the probability that you win at least $2 if you toss tails. (4 pts) (b) What is the total probability that you win $2 playing this game? (3 pts) (c) If you win at least $2, what is the probability you tossed heads? (3 pts)