• Calculate and interpret probabilities of simple and compound events.
• Describe the meaning of mutually exclusive and independence using probability.

[latex]P(\text{event}) = \dfrac{\text{number of outcomes in event}}{\text{number of all possible outcomes}}[/latex]

Facts about probabilities:

• The probability of a certain event (an event that will happen) is equal to [latex]1[/latex].
• The probability of an impossible event is equal to [latex]0[/latex]. This means that there are no possible outcomes for that event.
• Probabilities range from [latex]0[/latex] to [latex]1[/latex], including [latex]0[/latex] and [latex]1[/latex]. So, for any event [latex]\text{A}[/latex], [latex]0\leq P(\text{A})\leq1[/latex].
• Probabilities can be expressed as decimals, fractions, or percentages.

The sample space of an experiment is the set of all possible outcomes. Because the sample space consists of all of the outcomes, [latex]P(\text{sample space}) = 1 = 100\%[/latex].

Complement of an Event

The complement of event [latex]A[/latex] is denoted [latex]A'[/latex] (read “[latex]A[/latex] prime”) or [latex]A^c[/latex] (read “[latex]A[/latex] complement”). The complement of the event [latex]A[/latex] consists of all outcomes that are NOT in [latex]A[/latex].

More generally, for any event [latex]A[/latex], we can think of the probability of complements as having the following relationship:

[latex]P[/latex]([latex]A[/latex]) + [latex]P[/latex](not [latex]A[/latex]) = [latex]1[/latex]

or

[latex]P[/latex]([latex]A[/latex]) + [latex]P[/latex]([latex]A'[/latex]) = [latex]1[/latex]

The equation can also be rewritten as follows: [latex]P[/latex](not [latex]A[/latex]) = [latex]1[/latex] – [latex]P[/latex]([latex]A[/latex])