23 terms

AP Statistics: Probability

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Chance experiment
Any process that generates observations whose outcomes cannot be predicted with certainty
Sample space
Set of all possible outcomes of a chance experiment
Event
An outcome or set of outcomes of a chance experiment
Simple event
An event that consists of exactly one outcome
Complement
An event that contains the set or outcomes not included by a second event;
Find the complement by subtracting

Complement = 1 - probability(event)
Intersection
The set of all elements that are common to 2 or more sets.
Union
Set of all elements that are contained in 2 or more sets
Venn Diagram
A diagram that uses circles to display elements of different sets; overlapping circles show common elements
Disjoint
Two non-overlapping sets; aka mutually exclusive events
Mutually exclusive
Events that cannot happen at the same time
Probability of an event
Number of favorable outcomes divided by the total number of possible outcomes
Law of large numbers
As the number of repetitions of a probability experiment increases, the empirical probability (the proportion with which a certain outcome is observed) gets closer to the theoretical probability of the outcome
general addition rule
For any two events, A and B, the probability of A OR B is the probability of A and B minus their joint probability

P(A U B) = P(A) + P(B) - P(A and B)
General Multiplication Rule for Any Two Events
For any two events, A and B, the probability of A and B is the probability of A times the probability of B occurring given that A has occurred
Independent Events
Two or more events for which the outcome of one event does not affect the probability of the other; P(A) = P(A | B)
Dependent Events
Two or more events in which the occurrence of one event affects the probability of the other events; do not always possess a cause-and-effect relationship
Sampling without replacement
Removes each selected element from the population before the next selection is made to guarantee no element appears more than once in a single sample; probability of selecting any outcome changes after each selection
Sampling with replacement
Once an element has been included in the sample, it is returned to the population and may be selected again; probability of selecting any outcome remains constant
10% sampling condition
When sampling without replacement, the change in the probability of an outcome can be regarded as insignificant and thus ignored when sampling less than 10% of a population
Conditional Probability
Probability of an event occurring given that another event is known to have occurred; denoted as P(A | B)
Empirical probability
Probability that is based on simulation, experimentation or testing; the relative frequency of a successful outcome among those trials
Simulation
Modeling a problem situation or event that would be too difficult or impractical to actually perform; often used to calculate empirical probabilities
Table of Random Digits
Long string of digits (0 to 9) where the digits are independent of each other (knowing one digit does not give any knowledge to predicting another digit) and where any digit (0 to 9) has an equal chance of occurring as the next digit; used for probability simulations, random selection and random assignment
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