# 3.6: Chapter 3 Key Terms

- Page ID
- 79010

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- Conditional Probability
- the likelihood that an event will occur given that another event has already occurred

- Contingency Table
- the method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; the table provides an easy way to calculate conditional probabilities.

- Dependent Events
- If two events are NOT independent, then we say that they are dependent.

- Equally Likely
- Each outcome of an experiment has the same probability.

- Event
- a subset of the set of all outcomes of an experiment; the set of all outcomes of an experiment is called a sample space and is usually denoted by
*S*. An event is an arbitrary subset in*S*. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, and the like. Standard notations for events are capital, italicized letters such as*A*,*B*,*C*, and so on.

- Experiment
- a planned activity carried out under controlled conditions

- Independent Events
- The occurrence of one event has no effect on the probability of the occurrence of another event. Events A and B are independent if one of the following is true:
- \(P(A|B) = P(A)\)
- \(P(B|A) = P(B)\)
- \(P(A \cap B) = P(A)P(B)\)

- Mutually Exclusive
- Two events are mutually exclusive if the probability that they both happen at the same time is zero. If events A and B are mutually exclusive, then \(P(A \cap B) = 0\).

- Outcome
- a particular result of an experiment

- Probability
- a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; the foundation of statistics is given by the following 3 axioms (by A.N. Kolmogorov, 1930’s): Let
*S*denote the sample space and*A*and*B*are two events in*S*. Then:- \(0 ≤ P(A) ≤ 1\)
- If
*A*and*B*are any two mutually exclusive events, then \(P(A \cup B) = P(A) + P(B)\). - \(P(S) = 1\)

- Sample Space
- the set of all possible outcomes of an experiment

- Sampling with Replacement
- If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once.

- Sampling without Replacement
- When sampling is done without replacement, each member of a population may be chosen only once.

- The Complement Event
- The complement of event
*A*consists of all outcomes that are NOT in*A*.

- The Conditional Probability of \(A | B\)
*P*(A|B) is the probability that event*A*will occur given that the event*B*has already occurred.

- The Intersection: the \(\cap \) Event
- An outcome is in the event \(A \cap B\) if the outcome is in both \(A \cap B\) at the same time.

- The Union: the \(\cup\) Event
- An outcome is in the event \(A \cup B\) if the outcome is in
*A*or is in*B*or is in both*A*and*B*.

- Tree Diagram
- the useful visual representation of a sample space and events in the form of a “tree” with branches marked by possible outcomes together with associated probabilities (frequencies, relative frequencies