### Home > INT2 > Chapter 3 > Lesson 3.1.5 > Problem3-66

3-66.

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?

Refer to the table.

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

Refer to the table.

$6$ ways

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

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?

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

Insert the sums into the table in the eTool below to help you find the probabilities in parts (a) - (d).
Click the link at right for the full version of the eTool: Int2 3-66 HW eTool