- Calculate and interpret probabilities of simple and compound events.
- Understand the concept of mutually exclusive events.
Probability Properties
- For any two events, [latex]A[/latex] and [latex]B[/latex]: [latex]P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)[/latex]
- Two events are mutually exclusive if the probability that they both happen at the same time is zero. That is, if events [latex]A[/latex] and [latex]B[/latex] are mutually exclusive, then [latex]P(A \ \mathrm{and} \ B) = 0[/latex].
Therefore, [latex]P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = P(A) + P(B) - 0 = P(A) + P(B)[/latex]
Watch the following video to explain how you can use the probability property above:
So, when can we just add probabilities?
(a)
What is the probability it is a heart AND a spade?
(b) What is the probability it is a heart OR a spade?