Probability

Let's start with an example to introduce the vocabulary which is common in probability theory. Assume you are playing a game in which the players roll a die.

• The result of rolling a die is called outcome. For example, suppose you rolled the die and get the value 6. In this case, the outcome is 6.
• What are all possible outcomes of rolling a die? It has to be one the elements in \(\{1,2,3,4,5,6\}\). This is called the sample space and is usually denoted by \(\Omega\).
• A subset of \(\Omega\) is called an event. For example, \(\{2, 6\}\) is an event.
• The simple event is just one member of sample space. For instance, \(1\) is a simple event.

• Outcome: result of an experiment.
• Sample Space: set of all possible outcomes.
• Event: a subset of sample space.
• Simple Event: a member of sample space.

In rolling a die, two events \(E = \{1, 3, 5\}\) and \(F = \{2, 4, 6\}\) cannot occur simultaneously. In this case, we say that \(E\) and \(F\) are mutually exclusive.