- Calculate and interpret probabilities of simple and compound events.
- Understand the concept of mutually exclusive events.
Choose Your Own Dataset
For this problem, you'll determine probabilities from your choice of tables.
Mutually Exclusive Events
When both events [latex]A[/latex] and [latex]B[/latex] do not occur or happen at the same time, we can say that event [latex]A[/latex] and event [latex]B[/latex] are mutually exclusive or disjoint.
To find the probability of event [latex]A[/latex] OR event [latex]B[/latex], add the probability of event [latex]A[/latex] and the probability of event [latex]B[/latex], as long as both events are mutually exclusive.
mutually exclusive
If event [latex]A[/latex] and event [latex]B[/latex] are mutually exclusive, then
[latex]P(A \text{ or } B) = P(A \cup B) = P(A)+P(B)[/latex]
(a) What is the probability that Klaus will go on vacation to New Zealand OR Alaska?
(b) What is the probability that Klaus will not go to New Zealand or Alaska for vacation?
Independent Events
Sometimes, there are pairs of events for which one event has no effect on the probability of another event occurring. When this is the case, we say the events are independent.
independent events
Two events are independent if the outcome of the first event does not influence the probability of the second event. We can test for independence using the rule:
[latex]P(A \text{ and } B)=P(A) \times P(B)[/latex]
The results of the survey are displayed in the following contingency table.
| Owns a laptop | Does not own a laptop | Total | |
| Owns a desktop | 20 | 20 | 40 |
| Does not own a desktop | 60 | 20 | 80 |
| Total | 80 | 40 | 120 |
Is owning a desktop independent of whether the student owns a laptop? Or is there a relationship between these two events?