Basic Concepts of Probability

Term Definition
Descriptive Statistics used to summarize or describe characteristics of data with tools such as frequency distributions, graphs, and measures of center and variation
Inferential Statistics used to make inference or generalizations about a population
Rare Event Rule for Inferential Statistics If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
Event any collection of results or outcomes of a procedure
Simple Event an outcome or an event that cannot be further broken down into simpler components
Sample Space for a procedure consists of all possible simple events; that is, the sample space consists of all outcomes that cannot be broken down any further
P probability
A, B, and C denotes specific events
P(A) denotes the probability of event A occurring
Rule 1: Relative Frequency Approximation of Probability conduct (or observe) a procedure, & count the number of times event A actually occurs. Based on these actual results, P(A) is approximated as follows:
P(A) = # of times A occurred divided # of times procedure was repeated
Rule 2: Classical Approach to Probability (requires equally likely outcomes) Assume that a given procedure has n different simple events & that each of those simple events has an equal chance of occurring. If event A can occur in s of these n ways, then
Rule 3: Subjective Probabilities P(A), the probability of event A, is estimated by using knowledge of the relevant circumstances
Law of Large Numbers as a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability
Probability Limits always express a probability as a fraction or decimal number between 0 & 1-impossible event is 0; certain to occur is 1. for any event A, the probability of A is between 0 & 1 inclusive. that is 0 < P(A) < 1
Complementary Events the complement of event A, denoted by A, consists of all outcomes in which the event A does not occur.