Probability Rules

addition rule for mutually exclusive events

P (A U B)= P(A) + P(B)

events can not occur together (add probabilities)

addition rule for non-mutually exclusive events

P(A U B) = P(A) + P(B) - P(A n B)

events can not occur together (add probabilities and subtract intersection)

test for mutually exclusive

P(A) + P(B) = 1

multiplication rule for independent events

P(A n B) = P(A) x P(B)

multiplication rule for dependent events

P(A n B) = P(A) x P(B I A) or P(A n B) = P(B) x P(B I A)

events in which one occurrence effects the other (multiply probability by conditional probability)

test for independence

P(A) x P(B) = P(A n B) independent

not equal: dependent

complement rule

1- P(A) or 1- P(B)

conditional probability

P(A I B) = P(A n B) / P(B)

P(B I A) = P(A n B)/ P(A)

permutations

P = n!/(x-n)!

asks about specific ranking and order

n! only multiply up to the # of x

combination

C= n!/x!(x-n)!

order doesn’t matter, asks about combinations

n! only multiply up to the # of x