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Fixing the Odds
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?
Scratch Cards
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?
In a Box
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
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. He repeats this many times, each time betting half the total money he has. After $2n$ plays he has won exactly $n$ times. Has he more money, the same amount or less money than he started with?
NRICH is part of the family of activities in the Millennium Mathematics Project.