A and B throw a die alternatively till one of them gets a 6 and wins the game. Find their respective probabilities of winning, if A starts first.

Explanation

To solve the problem of finding the probabilities of A and B winning the game when they throw a die alternately until one of them gets a 6, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Probabilities**:
- The probability of success (getting a 6) when throwing a die is \( P(S) = \frac{1}{6} \).
- The probability of failure (not getting a 6) is \( P(F) = 1 - P(S) = 1 - \frac{1}{6} = \frac{5}{6} \).

...