Key Concepts: Probabilities of Independent and Dependent Events

Independent Events

Two events are independent if the outcome of one does not affect the other.

P(A and B) = P(A) × P(B)

Dependent Events

Two events are dependent if the outcome of one affects the other.

P(A and B) = P(A) × P(B | A)

Conditional Probability

P(B | A) is the probability of B occurring given that A has occurred.

Examples

• Drawing cards with replacement → independent.
• Drawing cards without replacement → dependent.