Definition 1.
The sample space \(\Omega\) is the set of all possible results of an experiment. A single result is called an outcome. A collection of results is called an event.
The sample space \(\Omega\) is the set of all possible results of an experiment. A single result is called an outcome. A collection of results is called an event.
We roll a 6-sided die two times. What is \(\Omega\text{?}\)
We flip a coin three times. What is \(\Omega\text{?}\)
We pick a number between 1 and 10. What is \(\Omega\text{?}\)
Let \(A\) be a set. The symbol \(\in\) means "is an element of", as in \(a \in A\text{.}\) Given another set \(B\text{,}\) we say \(A\) is a subset of \(B\text{,}\) written \(A\subset B\text{,}\) to mean that every element of the set \(A\) is also an element of the set \(B\text{.}\)
Let \(A, B \subset \Omega\text{.}\)
The union is \(A \cup B = \{x \mid x \in A \text{ or } x \in B\}\text{.}\)
The intersection is \(A \cap B = \{x \mid x \in A \text{ and } x \in B\}\text{.}\)
The set difference is \(A - B = \{x \mid x \in A \text{ and } x \notin B\}\text{.}\)
The complement is \(A^c = \{x \in \Omega \mid x \notin A\}\text{.}\)
The empty set, written \(\emptyset\) or \(\{\}\text{,}\) contains no elements.
Some more text.