Probability Rules

Complement Rule

P(A^c) = 1 - P(A)

Addition Rule for Mutually Exclusive Events

If A and B are mutually exclusive, P(A or B) = P(A) + P(B)

General Addition Rule for Two Events

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

Conditional Probability

The probability that one event happens given that another event is already known to have happened

Formula for Conditional Probability

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

General Multiplication Rule

The probability that events A and B both occur

General Multiplication Rule Formula

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

Independent Events

If the occurrence of one event does not change the probability that the other event will happen

Independent Formula

P(A and B) = P(A) x P(B)

P(A and B)

Multiply - P(A) x P(B)

P(A or B)

Add - P(A) + P(B)

Example of Selecting Two Things

Multiply the probability by each other (e.g., 0.56 x 0.56)

Mutually Exclusive (Disjoint)

They have no outcomes in common and can never occur together - P(A and B) = 0