# Conditional Probability Question

Conditional Probability Question Solution - 24 June

You are playing a probability game with your friend using a fair coin. Both of you decide a particular sequence that you have to achieve.

Let us suppose you chose the sequence to be: H T H
Your friend chose the sequence to be: H T T

Now you keep tossing coin until you get the sequence and the same is done by your friend. You keep doing that till you achieve your predefined sequence and keep writing the result on paper. At the end of the game the player whose average number of tosses will be lowest, he will win.

The results of game 1 toss:
You: H T T H T H
Your friend: H T H H H T H H T T

The results of game 2 toss:
You: T T H T T H H T H
Your friend: T T H H T H T T

The results of game 3 toss:
You: T T H H T H
Your friend: H H T H T T

Now after 3 games, your average score is 7 and your friend's average score is 8. Now assume that you keep playing the game and play many a times. What will be the possible outcome out of the following?

a) You win
c) Tie