The game is that I and my opponent keep on tossing a fair coin alternatively until a tails shows up. When first tails is seen the game stops and whoever got that tails wins the game.
I calculated the expected number of coin tosses to end the game and it comes out to be 2. But the question is whether the below statement is true?
The probability of the above game ending within finite number of tosses is equal to 1.
Please provide your answer and the arguments supporting the answer.