## Probability

### Definitions

- Probability Experiment
- Process which leads to well-defined results call outcomes
- Outcome
- The result of a single trial of a probability experiment
- Sample Space
- Set of all possible outcomes of a probability experiment
- Event
- One or more outcomes of a probability experiment
- Classical Probability
- Uses the sample space to determine the numerical probability that an event will happen.
Also called theoretical probability.
- Equally Likely Events
- Events which have the same probability of occurring.
- Complement of an Event
- All the events in the sample space except the given events.
- Empirical Probability
- Uses a frequency distribution to determine the numerical probability. An empirical
probability is a relative frequency.
- Subjective Probability
- Uses probability values based on an educated guess or estimate. It employs opinions
and inexact information.
- Mutually Exclusive Events
- Two events which cannot happen at the same time.
- Disjoint Events
- Another name for mutually exclusive events.
- Independent Events
- Two events are independent if the occurrence of one does not affect the probability of
the other occurring.
- Dependent Events
- Two events are dependent if the first event affects the outcome or occurrence of the
second event in a way the probability is changed.
- Conditional Probability
- The probability of an event occurring given that another event has already occurred.
- Bayes' Theorem
- A formula which allows one to find the probability that an event occurred as the result
of a particular previous event.
- Factorial
- A positive integer factorial is the product of each natural number up to and including
the integer.
- Permutation
- An arrangement of objects in a specific order.
- Combination
- A selection of objects without regard to order.
- Tree Diagram
- A graphical device used to list all possibilities of a sequence of events in a systematic
way.

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James Jones