Toss the Coin

If you toss a coin 10 times and it lands heads up every time, what are the chances it will land heads up if you toss it again?




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Ten seconds later... John replied I got it.

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You are playing a probability game with your friend using a fair coin. Both of you decide on 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 coins 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 the game 1 toss:
You: H T T H T H
Your score: 6
Your friend: H T H H H T H H T T
Your friends' score: 10

The results of the game 2 toss:
You: T T H T T H H T H
Your score: 9
Your friend: T T H H T H T T
Your friends' score: 8

The results of the game 3 toss:
You: T T H H T H
Your score: 6
Your friend: H H T H T T
Your friends' score: 6

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 times. What will be the possible outcome of the following?

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Chhote se Chintu Miyan,
Lambi si Pooch.
Jahan Jaye Chintu Miyan,
Wahan Jaye Pooch.

छोटे से चींटू मियाँ,
लंबी सी पूंछ।
जहाँ जाये चींटू मियाँ,
वहाँ जाये पूंछ।

Bolo kya?

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What is the chance of Mr John now?

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Gambling

In Canada, a mathematical puzzle must be solved in order to win the lottery to classify it as a “game of skill” not gambling.