Cue Column:
- What does P(A|B) measure?
- How to check independence?
- Are mutually exclusive events independent?
Note Column: P(A|B) = P(B) gives the probability of A given B has occurred. Events A and B are independent iff P(A intersect B) = P(A)*P(B), equivalently P(A|B) = P(A). Critical fact: mutually exclusive events with non-zero probabilities are NEVER independent. If A and B are mutually exclusive, knowing B occurred means A definitely did not — so P(A|B) = 0, not P(A).
Summary: Conditional probability restricts the sample space. Independence means one event's occurrence doesn't affect the other. Mutual exclusivity implies dependence, not independence.