Bang or No Bang Game 2: Wheel of Fortune

The Wheel of Fortune is just like a coin, but with twenty faces rather than two! The probabilty of guessing which section the wheel will stop on is much smaller than the probability of guessing whether a coin will fall heads or tails. Why is this?

It is because there are far more ways that you can be wrong than right! On a 20-section wheel of fortune, like the one that appears in the show "Bang or No Bang: The Science of Risk", the probability that you will guess the right section is one-in-twenty.

In other words the probability, P, of guessing the right section is

(number of favourable outcomes) divided by (total number of possible outcomes)

or

P = 1 / 20 = 0.05

This means that you have a 5% chance of guessing correctly.

How can you increase the chance of being right? You can either increase the number of ways you can be right, or decrease the number of ways you can be wrong!

In other words, if you allow yourself two sections rather than one, you double your chances of being right!

In the wheel of fortune pictured here, which one colour should you pick as the winning colour? What is the probability of you being right if you guess this colour?

If you are given two colours, which two should you choose? What is your probability then?

Can you work out the probabilities of each colour, and each combination of colours?