A First Course in Statistics, 12th Edition

3.6 The Multiplicative Rule and Independent Events

The probability of an intersection of two events can be calculated with the multiplicative rule, which employs the conditional probabilities we defined in the previous section. Actually, we’ve already developed the formula in another context. Recall that the conditional probability of B given A is

[&P|pbo|B|pipe|A|pbc||=|*frac*{P|pbo|A|inter|B|pbc|}{P|pbo|A|pbc|} &]

$$P(B|A)={\displaystyle \frac{P(A\cap B)}{P(A)}}$$

Multiplying both sides of this equation by P(A), we obtain a formula for the probability of the intersection of events A and B. This formula is often called the multiplicative rule of probability.

Multiplicative Rule of Probability

$P(A\cap B)=P(A)P(B|A)$ or, equivalently, $P(A\cap B)=P(B)P(A|B)$

Example 3.16 The Multiplicative ...