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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

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a set of numbered balls used for a game:
 

 Set of balls: 2, 3, 4, 5, 6

To play the game, the balls are mixed up and two balls are randomly picked out together. For example:

one ball numbered 4 and one ball numbered 5
The numbers on the balls are added together: $4 + 5 = 9$

If the total is even, you win. If the total is odd, you lose.

How can you decide whether the game is fair?
 
Here are three more sets of balls:
 
 Set B: 1,3,5,6,7 Set C: 2,3,4,5,6,8 Set D 1,3,4,5,7,9


Which set would you choose to play with, to maximise your chances of winning?

What proportion of the time would you expect to win each game?

Test your predictions using the interactivity.

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Is it possible to produce a fair game?
Can you find a set of balls where the chance of getting an even total is the same as the chance of getting an odd total?

Can you find more than one such set?