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?
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?
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
Chris and Jo decide to play a game.
They put two red and four blue ribbons in a box.
They each pick a ribbon from the box without looking (and without replacing them).
Jo wins if the two ribbons are the same colour and Chris wins if the two ribbons are a different colour.
Is the game fair?
If not, how many ribbons of each colour would you need in the box to make it a fair game?
Is there more than one way to make a fair game?
This problem is based on one offered by Doug Williams at the 2003 ATM conference in Bath UK. See also http://www.blackdouglas.com.au/taskcentre
Click here for a poster of this problem.