Probability rules, conditional probability and independence

Learning objectives

Interpret a probability as a long-run relative frequency, describe what the law of large numbers says about that relative frequency, and estimate a probability by designing and carrying out a simulation with a stated rule for assigning outcomes

List the outcomes in a sample space, calculate the probability of an event from equally likely outcomes, and use the complement rule P(not A) = 1 − P(A)

Identify mutually exclusive events as those with P(A and B) = 0, and calculate the probability of a union with the addition rule P(A or B) = P(A) + P(B) − P(A and B)

Calculate a conditional probability from P(A | B) = P(A and B) ÷ P(B) or directly from a two-way table, and apply the general multiplication rule P(A and B) = P(A) × P(B | A), using a tree diagram in a multi-stage setting

Determine whether two events are independent by checking whether P(A | B) = P(A) or whether P(A and B) = P(A) × P(B), and distinguish independent events from mutually exclusive events