A and B throw alternately a pair of dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. Find their respective chance of winning, if A begins.

Explanation

To solve the problem, we need to calculate the probabilities of A and B winning the game based on the conditions given. Let's break it down step by step.

### Step 1: Calculate the probabilities of rolling a 6 and a 7 with two dice.

1. **Probability of rolling a sum of 6 (P(6))**:
- The possible combinations to get a sum of 6 are:
- (1, 5)
- (2, 4)
...