Three persons A, B, C throw a die in succession till one gets a six and wins the game. Find their respective probabilities of wining , if A begins.

Explanation

To find the probabilities of A, B, and C winning the game when they throw a die in succession until one of them gets a six, we will analyze the situation step by step.

### Step 1: Define the Probabilities
Let \( P(A) \), \( P(B) \), and \( P(C) \) be the probabilities that A, B, and C win, respectively.

### Step 2: Calculate A's Winning Probability
A can win in several scenarios:
1. A wins on the first throw.
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