### Win or Lose?

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?

### 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?

# Introducing Distributions

##### Stage: 4 Challenge Level:

The key idea in all this is to see how a probability distribution gives a theoretical description of the random situation, but that this does not mean that our sample data must match it.

You will also see how larger samples often get closer to the theoretical distribution but that the sample is not compelled to behave like that (it's random after all), although it's a rare event when it doesn't.