Theoretical probability

problem
Win or lose?

Age

14 to 16

Challenge level

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?
problem
Coin tossing games

Age

14 to 16

Challenge level

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?
problem
Marbles and bags

Age

14 to 16

Challenge level

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?
problem
Gambling at Monte Carlo

Age

14 to 16

Challenge level

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
problem
Teams

Age

16 to 18

Challenge level

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.
problem
Snooker frames

Age

16 to 18

Challenge level

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?
problem
Snooker

Age

16 to 18

Challenge level

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?
problem
Squash

Age

16 to 18

Challenge level

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?
problem
Knock-out

Age

16 to 18

Challenge level

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?
problem
Rain or shine

Age

16 to 18

Challenge level

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.