Multiplication Rule

The multiplication rule determines the probability of two events happening together (the intersection). It multiplies the probability of one event by the conditional probability of the second event, given that the first has occurred.

Example: If 5% of people have a certain disease, and the test is 90% accurate for those with the disease, then the probability of having the disease and testing positive is 5% × 90% = 4.5%.

For any two events A and B, the probability of their intersection is given by:

P(A ∩ B) = P(A|B)P(B) = P(B|A)P(A).

For independent events, this simplifies to P(A ∩ B) = P(A)P(B).

The chain rule extends this to multiple events.