A and B toss coin alternately till one of them gets a head and wins the game. If A starts first, find the probability the B will win the game.

Explanation

To find the probability that B will win the game when A and B toss a coin alternately, we can follow these steps:

### Step 1: Understand the game structure
A starts the game by tossing a coin. If A gets a head (H), A wins immediately. If A gets a tail (T), then B gets a chance to toss the coin. If B gets a head, B wins. If B gets a tail, the game goes back to A, and the process repeats.

### Step 2: Define probabilities
The probability of getting a head (H) on any toss is \( P(H) = \frac{1}{2} \).
The probability of getting a tail (T) on any toss is \( P(T) = 1 - P(H) = \frac{1}{2} \).
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