Probability

problem
Thank your lucky stars

Age

14 to 16

Challenge level

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?
problem
Penta colour

Age

14 to 16

Challenge level

In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?
problem
Scratch cards

Age

14 to 16

Challenge level

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?
problem
Fixing the odds

Age

14 to 16

Challenge level

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?
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?