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4-96.

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?

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?

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

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: CCG 4-96 HW eTool