Sections

Key Terms
# Key Terms

- 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 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*AND*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*AND*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 three axioms (by A.N. Kolmogorov, 1930s): 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*OR*B*) =*P*(*A*) +*P*(B), and *P*(*S*) = 1

- 0 ≤

- 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 AND event
- an outcome is in the event
*A*AND*B*if the outcome is in both*A*AND*B*at the same time

- the complement event
- the complement of event
*A*consists of all outcomes that are NOT in*A*

- the conditional probability of one event GIVEN another event
*P*(*A*|*B*) is the probability that event*A*will occur given that the event*B*has already occurred

- the OR event
- an outcome is in the event
*A*OR*B*if the outcome is in*A*or is in*B*or is in both*A*and*B*

- the OR of two events
- an outcome is in the event
*A*OR*B*if the outcome is in*A*, 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)

- Venn diagram
- the visual representation of a sample space and events in the form of circles or ovals showing their intersections