A player in the casino dice game described in problem 4-10 rolled a sum of $6$ on his first roll. He will win if he rolls a sum of six on the second roll but lose if he rolls a sum of seven. If anything else happens they ignore the result and he gets to roll again.  

1. How many ways are there to get a sum of six?

   Hint (a):

   Refer to the table.

2. How many ways are there to get a sum of seven?

   Hint (b):

   Refer to the table.

   Answer (b):

   $6$ ways

3. How many possible outcomes are important in this problem?

   Hint (c):

   How many ways are there to roll a sum of $6$ or a sum of $7$?

4. What is the probability of getting a sum of six before a sum of seven?

   Hint (d):

   $\large\frac{\text{# of ways to get a sum of six}}{\text{total of important}}$