Choosing the correct sample space

When one element is chosen uniformly at random from a finite universal set, every element is equally likely and \(\mathrm P(A)=\dfrac{n(A)}{n(\xi)}\). Count the required region for the numerator and the actual sampling pool for the denominator.

If the sampling pool changes, recalculate both counts. For example, selecting from everyone and selecting only from members of A are different experiments.

A Venn diagram of face labels shows which labels occur on two dice. It does not list the outcomes when both dice are thrown. For independent fair dice, use the equally likely ordered pairs of faces to count matching outcomes.

Do not use the number of distinct labels in a union as the denominator for a two-dice experiment.