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Probability	A number from 0 to 1 telling how likely an event is		math-probability-terms
Impossible event	Probability 0		math-probability-terms
Certain event	Probability 1		math-probability-terms
Outcome	One possible result of an experiment		math-probability-terms
Event	A set of outcomes		math-probability-terms
Sample space	The set of all possible outcomes		math-probability-terms
Experiment (trial)	An action with an uncertain result, like rolling a die		math-probability-terms
Theoretical probability	Favorable outcomes divided by all equally likely outcomes		math-probability-terms
Experimental probability	Number of times it happened divided by number of trials		math-probability-terms
Complement of an event	All outcomes where the event does not happen; P(not A) = 1 − P(A)		math-probability-terms
Independent events	One event does not change the probability of the other		math-probability-terms
Dependent events	One event changes the probability of the other		math-probability-terms
Mutually exclusive events	Events that cannot happen at the same time		math-probability-terms
Multiplication rule (independent)	P(A and B) = P(A) × P(B)		math-probability-terms
Addition rule	P(A or B) = P(A) + P(B) − P(A and B)		math-probability-terms
Conditional probability	P(A | B) = P(A and B) / P(B)		math-probability-terms
Bayes' theorem	P(A | B) = P(B | A) P(A) / P(B)		math-probability-terms
Law of large numbers	With many trials, experimental probability gets close to theoretical probability		math-probability-terms
Expected value	The long-run average: sum of each value times its probability		math-probability-terms
Random variable	A variable whose value comes from a random process		math-probability-terms
Probability of heads on a fair coin	1/2		math-probability-terms
Probability of a 4 on a fair die	1/6		math-probability-terms
Probability of an even number on a die	1/2		math-probability-terms
Probability of a heart from a standard deck	13/52 = 1/4		math-probability-terms
Probability of an ace from a standard deck	4/52 = 1/13		math-probability-terms
Cards in a standard deck	52		math-probability-terms
Probability of two heads in two fair flips	1/4		math-probability-terms
Probability of a sum of 7 with two dice	6/36 = 1/6		math-probability-terms
Number of outcomes when rolling two dice	36		math-probability-terms
Number of outcomes in 3 coin flips	8		math-probability-terms
Fundamental counting principle	Multiply the number of choices at each step		math-probability-terms
Outfits from 3 shirts and 4 pants	12		math-probability-terms
Factorial n!	n × (n − 1) × ... × 1		math-probability-terms
Permutation	An ordered arrangement		math-probability-terms
Permutation formula	P(n, r) = n! / (n − r)!		math-probability-terms
Combination	A selection where order does not matter		math-probability-terms
Combination formula	C(n, r) = n! / (r!(n − r)!)		math-probability-terms
Ways to arrange 5 books on a shelf	5! = 120		math-probability-terms
P(5, 2)	20		math-probability-terms
C(5, 2)	10		math-probability-terms
C(6, 3)	20		math-probability-terms
C(10, 2)	45		math-probability-terms
C(n, 0) and C(n, n)	Both equal 1		math-probability-terms
Pascal's triangle	A triangle where each number is the sum of the two above it; rows give combinations		math-probability-terms
Binomial distribution	The distribution of the number of successes in a fixed number of independent yes/no trials		math-probability-terms
With replacement	Each item is put back before the next draw		math-probability-terms
Without replacement	Items are not put back; later probabilities change		math-probability-terms
Tree diagram	A branching picture that lists outcomes of a multi-step event		math-probability-terms
Venn diagram	Overlapping circles showing how sets share members		math-probability-terms
Odds	Ratio of favorable outcomes to unfavorable outcomes		math-probability-terms
Fair game	A game where each player has the same expected value		math-probability-terms
Simulation	Using random numbers or objects to imitate a real chance process		math-probability-terms