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# Elem Stats ch 4

### A Brief Version: Elementary Statistics ch 4

Probability Experiment A chance process that leads to well-defined results called outcomes.
Outcome The result of a single trial of a probability experiment.
Sample Space The set of all possible outcomes of a probability experiment.
Tree Diagram A device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment.
Event Consists of a set of outcomes of a probability experiment.
Simple Event An event with one outcome.
Compound Event Consists of two or more outcomes or simple events.
Equally Likely Events Events that have the same probability of occurring.
Classical Probability Assumes that all outcomes in the sample space are equally likely to occur.
Probability Rule 1 The probability of any event E is a number (either a fraction or decimal) between and including 0 and 1.
Probability Rule 2 If an event E cannot occur (i.e., the event contains no members in the sample space), its probability is 0.
Probability Rule 3 If an event E is certain, then the probability of E is 1.
Probability Rule 4 The sum of the probabilities of all the outcomes in the sample space is 1.
Complement of an Event E The set of outcomes in the sample space that are not included in the outcomes of event E.
Empirical Probability Relies on actual experience to determine the likelihood of outcomes.
Law of Large Numbers When a probability experiment is repeated a large number of times, the relative frequency probability of an outcome will approach its theoretical probability.
Subjective Probability Uses a probability value based on an educational guess or estimate, employing opinions and inexact information.
Mutually Exclusive Events Two events cannot occur at the same time.
Addition Rule 1 When two events A and B are mutually exclusive, the probability that A or B will occur is P(A or B) = P(A) + P(B).
Addition Rule 2 If A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) - P(A and B).
Independent Events If there are two events A and B, and if A occurs it does not affect the probability of B occurring.
Multiplication Rule 1 When two events are independent, the probability of both occurring is P(A and B) = P(A)P(B)
Dependent Events When the outcome or occurrence of the first event affects the outcome or occurrence of second event in such a way that the probability is changed.
Conditional Probability An event B in relationship to an event A is the probability that event B occurs after event A has already occurred.
Multiplication Rule 2 When two events are dependent, the probability of both occurring is P(A and B) = P(A) x P(B|A).
Fundamental Counting Rule A rule that is used to determine the total number of possibilities in a sequence of events.
n! = n(n-1)(n-2).....1
0! = 1
Permutation An arrangement of n objects in a specific order.
Combination A selection of distinct objects without regard to order.
Created by: dengler