Use a probability area model, a tree diagram, or refer to the table you created for the Roll and Win situation (problem 3-6) that represents the sample space for the sum of the numbers when rolling two standard six-sided dice.

1. In a standard casino dice game the player wins on the first roll if he rolls a sum of $7$ or $11$. What is the probability of winning on the first roll?

   Answer (a):

   $\frac{8}{36}$

2. The player loses on the first roll if he rolls a sum of $2, 3,$ or $12$. What is the probability of losing on the first roll?

   Hint (b):

   Use the table.

3. If the player rolls any other sum, he continues to roll the dice until the first sum he rolled comes up again or until he rolls a sum of $7$ or $11$, whichever happens sooner. What is the probability that the game continues after the first roll?

   Hint (c):

   What is the complement of the events in parts (a) and (b)?