A player in the casino dice game described in Roll and Win (problem 3-6) rolled a sum of six 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, the result is ignored 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):

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