"Craps" is a gambling game played with two standard, six-sided dice. One of several available bets at craps is the "Pass" bet. Here, two dice are rolled. If they total 7 or 11, the bet is won immediately; if they total 2, 3, or 12, the bet is lost immediately. Any other number becomes the player's "point." In this case, the player continues to roll until either he rolls his "point" (in which case the bet is won), or rolls a 7 (in which case the bet is lost).

a) You win the "pass" bet on your first roll, if that first roll is a 7 or an 11. What is the probability of this happening?

b) If you didn't win the "pass" bet on your first roll, you still have a chance. If that first roll was a 4, 5, 6, 8, 9, or 10, you will continue to roll. You must get that initial number again, before you roll a 7. Let's work out one of the scenarios. First off, what is the probability your initial roll was a 6?

c) If that initial roll was a 6, you will now keep rolling until you get another 6 (in which case you win), or a 7 (in which case you lose). Any other outcome can be ignored for now. What is the probability that you roll a 6 before you roll a 7?

d) Now put the pieces together: What is the overall probability of winning a "pass" bet at craps?