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If you can do one task n number of ways and a second m number of ways, then both tasks can be done in n*m ways.

Multiplication principle

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The P(A) of any event is between 0 and 1 (inclusive)

Probability rule 1

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If S is the sample space in a probability model, then P(S)=1

Probability rule 2

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Two events A and B are disjoint if they have no outcomes in common. P(A or B)=P(A)+P(B)

Probability rule 3

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the complement of A is 1-P(A)

Probability rule 4

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P(A and B) = P(A)*P(B)

Multiplication rule for independent events

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P(A or B) = P(A)+P(B) - P(A and B)

General addition rule for unions of two events

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P(B|A) = P(A and B)/P(A)

Conditional probability

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if P(B|A) = P(B)

Independent events

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random variable with either a finite (whole) number value or a countable number

Discrete random variable

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takes all values in an interval of numbers, described by a density curve.

Continuous random variable

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mean of X = multiply each possible value by its probability and then add it up

Mean of a discrete random variable

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variance of x = (x1-mean)^2**p1...(xi-mean)^2**pi

Variance of a discrete random variable

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if X is a random variable and a and b are fixed numbers, mean of a+bX = a+bmeanX

rule 1 for means

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if X and Y are random variables, meanx+y=meanx + meany

rule 2 for means

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bcdf(n, p, k)

bcdf on calculator

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mean = np

mean of binomial

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Sx=sqrt(npq)

std. dev of binomial

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gcdf(p,n)

gcdf on calculator

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mean = 1/p

Mean of geometric random variable

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q/p^2

std. dev of geometric random variable

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P(X>n) = q^n

probability of more than n trials before success

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