• Probability – the likelihood of the occurrence of an event
• Random outcome – an outcome that cannot be predicted with certainty
• Statistical experiment or observation – any activity that results in a definite, but random, outcome
• Simple event – the most basic outcomes in a sample space; cannot be broken down any further
• Event – any simple event or collection of simple events in a sample space
• Sample space – the collection of all simple events for a statistical experiment
▪ The sample space is a collection of equally likely outcomes
Empirical Probability (relative frequency)
▪ The outcomes of a random experiment are observed over repeated trials
Note: the Law of Large Numbers states that relative frequency gets closer and closer to the true probability as the sample size increases
▪ The probability of any event is a person’s opinion (educated guess? intuition?) of the likelihood of an event
P(A) = whatever you think it is!
1. The probability of any event must be between 0 and 1. That is, [pic] for any event A.
2. The sum of the probabilities for all simple events in a sample space must be 1.
3. The complement of event A consists of all outcomes in the sample space that do not make up event A, therefore
Note: A Venn diagram is useful for displaying relationships among events in a sample space.
The Venn diagram to show A and AC might look like this:
4. Two events are mutually exclusive (or disjoint) if they contain no common outcomes.
The Venn diagram to show two disjoint events A and B might look like this:
5. The union of two events A and B consists of all outcomes in the sample space...