Biased events

So far we have only looked at fair dice. Fair dice have an equal probability of landing on each number. Dice are biased when not all of the numbers have an equal probability of being landed on. Dice can be made to be biased by changing the shape or by being constructed with weights inside.

Any event is biased when outcomes are not equally likely.

For a single fair dice, if X is the possible outcome of rolling the dice then X = {1, 2, 3, 4, 5, 6}.

If x is the actual outcome of any particular trial then we can show the probability of each outcome, P(X=x), in a table, like this.

If the dice is biased then the probability distribution will be different to this.

Below is a simulation of a biased dice. By doing an experiment, find the relative frequencies of the possible outcomes 1 to 6 to find out how the dice is biased.