Key Terms Chapter 3 - Statistics

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 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 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.

equally likely

Each outcome of an experiment has the same probability.

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.

Dependent events

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

the complement event

The complement of event A consists of all outcomes that are NOT in A.

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: 1. P(A|B) = P(A) 2. P(B|A) = P(B) 3. 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.

sampling without replacement

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

outcome

a particular result of an experiment

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.

sample space

the set of all possible outcomes of an experiment

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

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 OR B) = P(A) + P(B). -P(S) = 1

experiment

a planned activity carried out under controlled conditions

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.