1. (*)Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule to decide who will pay the bill. Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yield the same result, the bill will be shared by all. (It may be helpful to list the outcomes in the sample space)

(a) Find the probability that only you have to pay.

(b) Find the probability that all three will share.