http://www.ck12.org Chapter 3. An Introduction to Probability
3.5 Additive and Multiplicative Rules
Learning Objectives
- Calculate probabilities using the additive rule.
- Calculate probabilities using the multiplicative rule.
- Identify events that are not mutually exclusive and how to represent them in a Venn diagram.
- Understand the condition of independence.
When the probabilities of certain events are known, we can use those probabilities to calculate the probabilities of
their respective unions and intersections. We use two rules: the additive and the multiplicative rules to find those
probabilities. The examples that follow will illustrate how we can do so.
Example:
Suppose we have a loaded (unfair) die. We toss it several times and record the outcomes. If we define the following
events:
A:{observe an even number}
B:{observe a number less than 3}Let us suppose that we have come up withP(A) = 0. 4 ,P(B) = 0. 3 ,andP(A∩B) = 0 .1. We want to findP(A∪B).
Solution:
It is probably best to draw the Venn diagram to illustrate the situation. As you can see, the probability of the events
AandBoccurring is the union of the individual probabilities in each event.
Therefore,