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?
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?
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?
In the problem Odds and Evens, we introduced the following game and invited you to work out whether the game was fair:
Here is a set of numbered balls used for a game.
To play the game, the balls are mixed up and two balls are randomly picked out together.
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?
How many sets of balls with this property can you find?
What do you notice about the number of odd and even balls in your sets?