• Calculate and interpret probabilities of simple and compound events.
• Understand the concept of mutually exclusive and independent events.

AND ([latex]\cap[/latex]) vs. OR ([latex]\cup[/latex])

There are times when you want to combine two events by using the word AND or the word OR. In statistics, specifically in probability, there is an important distinction between the words AND and OR. 

“AND” events

AND ([latex]\cap[/latex]) means that both events must happen.

[latex]P(A \text{ and }B)= P(A \cap B)=[/latex] the relative frequency of events [latex]A[/latex] and [latex]B[/latex] must happen in the same outcome.

“OR” events

An outcome is in the event [latex]A[/latex] OR [latex]B[/latex] if the outcome is in [latex]A[/latex] or is in [latex]B[/latex] or is in both [latex]A[/latex] and [latex]B[/latex].

[latex]P(A \text{ or }B)= P(A \cup B)=[/latex] the relative frequency of either event [latex]A[/latex] or [latex]B[/latex] (or both) must happen in the outcome.

To find the probability of event [latex]A[/latex] OR event [latex]B[/latex] in a two-way table, add all frequencies of event [latex]A[/latex] and event [latex]B[/latex] and divide it by the total.

In the example, the number of students who like Oatmeal cookies is [latex]39[/latex] and the number of students who like Chocolate Chip cookies is [latex]45[/latex] but the number of students who prefer Oatmeal OR Chocolate Chip is not [latex]39+45=84[/latex] because this would include the [latex]36[/latex] students who like both twice. 

Do not double count the frequency when both events [latex]A[/latex] and [latex]B[/latex] occur.