$\textbf{Coin Toss}$
Joe tosses a coin. If he gets heads, he stops, otherwise he tosses again. If the second toss is heads, he stops. Otherwise, he tosses the coin again. The process continues until either he gets heads or $100$ tosses have been done. What is the ratio of heads to tails in all the possible scenarios?
$\textbf{Answer}$
$1:1$
$\textbf{Analysis}$
We can start by considering the case when the game will stop after $1$ toss, $2$ tosses, $3$ tosses, etc. It is easy to see the answer is always $1:1$. This conclusion can also be clearly shown in the following probability tree (This chart only shows $4$ tosses, but the conclusion still applies for up to $100$ tosses):
$\textbf{Note}$
The probability tree is an intuitive and powerful tool.