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Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

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Win or Lose?

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

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Thank Your Lucky Stars

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?

Odds and Evens Made Fair

Age 14 to 16 Challenge Level:

If I had 1 odd and 1 even ball would it be a fair game?
If I had 2 odds and 1 even ball would it be a fair game?
If I had 1 odd and 2 even balls would it be a fair game?
If I had 1 odd and 3 even balls would it be a fair game?
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