1. [To diet or not to diet] Cookie Monster wants to eat a cookie but needs to go on a diet. So he decides to toss a fair coin to decide whether or not to eat the cookie. He will eat the cookie if the toss is heads. If the toss is tails, he does not give up immediately, but decides to ip the coin two more times. If the subsequent two tosses are both heads, then he eats the cookie. If not, he is good and refrains from eating the cookie. (a) Find the probability that Cookie Monster eats the cookie. (b) What is the probability that the rst toss is heads, given that Cookie Monster eats the cookie