Combining probabilities

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
Favourite

At Least One...

Age

11 to 14

Challenge level

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?
problem
Favourite

The Better Choice

Age

14 to 16

Challenge level

Here are two games you can play. Which offers the better chance of winning?
problem

Odd Dice

Age

14 to 16

Challenge level

These strange dice are rolled. What is the probability that the sum obtained is an odd number?
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
Favourite

Same Number!

Age

14 to 16

Challenge level

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
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

Voting Paradox

Age

14 to 18

Challenge level

Some relationships are transitive, such as 'if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?
problem

Do You Brush Your Teeth Every Day?

Age

14 to 18

Challenge level

How can we find out answers to questions like this if people often lie?
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?