Multiplication rule of probability
The multiplication rule gives P(A and B) = P(A) × P(B given A), the joint probability of two events, simplifying to P(A) × P(B) when the events are independent.
See it move
A component passes the first visual inspection with probability 0.90. Given that it passes, the probability it also passes a stress test is 0.80, a conditional probability. Multiplying gives the joint probability of passing both: 0.90 × 0.80 = 0.72, or 72 per cent — the multiplication rule for two related events.
The formula
Variables
- Probability that event A occurs
- Conditional probability that B occurs given A has already occurred
- Joint probability that both A and B occur
General multiplication rule for the joint probability of two events; simplifies to P(A) × P(B) only when A and B are independent.
Check yourself
A logistics firm's packages pass through two checks. Check 1 detects no damage with probability 0.85. Given that a package passes Check 1, the (conditional) probability it also passes Check 2 undamaged is 0.95. What is the probability that a package passes both checks?