The Multiplication Rule of ProbabilityThe Multiplication Rule of Probability

We have already considered that if events A and B are independent then P(A and B) = P(A) *P(B). This formula is a special case of the more general probabilities multiplication rule:

It states that the probability of the joint occurrence of two events, A and B, is equal to the probability of event A multiplied by event B's conditional probability, given that event A has occurred.
Let's look at the example for a better understanding of this rule:

Assume you draw two cards from a standard deck (52 cards) without replacement. What is the probability of drawing a heart on the first card and a diamond on the second?
Event A - drawing a heart first. Event B - drawing a diamond second.


Pay attention that in the multiplication probabilities rule, the order in which events occur is unimportant - we can consider both the probability P(B)*P(A|B) and P(A)*P(B|A).

Everything was clear?

Section 2. Chapter 3