Probability

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 prize?

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

Heads or Tails - the prize doubles until you win it. How much would you pay to play?

A weekly challenge concerning combinatorical probability.

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

If you asked your mum/dad/friend to take you to the park today, what sort of response might you get?