Your friend proposes a game of chance. You roll a fair 6-sided die repeatedly until it lands on 1, at which point the game ends. Each time the roll does not land on 1, you pay your friend a random amount. The amount that you pay after each roll (including the roll on which you roll 1) is exponentially distributed with a mean of 1 dollar, and is independent of what you have paid on all of the others rolls (and the number of rolls).

(a) How much do you expect to pay in total after playing the game once?

(b) After playing the game once, what is the probability that you pay more than 10 dollars?