Lesson 3.2 Independent Events / Mutually Exclusive Events

Independent Events

A and B are independent events if the chance of A occurring does not affect B and the chance of B occurring does not affect A. To show that two events are independent, show only ONE of the following (If one is true then all three equations will be true):

• P(A|B) = P(A)
• P(B|A) = P(B)
• P(A AND B) = (P(A))( P(B))

Example: Let event A = taking a math class this term. Let event B = taking a science class this term.

Given: P(A) = 0.6, P(B) = 0.5, and P(A AND B) = 0.3.

Show that A and B are independent events.

To begin, notice that A AND B = taking a math class AND a science class this term.

Since P(A), P(B), and P(A AND B) are given, check to see if P(A AND B) = ((P(A))(P(B)).

P(A AND B) = 0.3.

(P(A))(P(B)) = (0.6)(0.5) = 0.3.

So, P(A AND B) = ((P(A))(P(B)).

Therefore, A and B are independent events.

Mutually Exclusive Events

A and B are mutually exclusive if they cannot happen at the same time. This means that A and B do not share any outcomes and

P(A AND B) = 0.

Example: Suppose you have won a vacation to either Africa or Australia but not both.

Let A = going to Africa and B = going to Australia.

P(A AND B)

= P(going to Africa AND going to Australia at the same time)

= 0

Therefore, A and B are mutually exclusive events.

Warning

• You must show that any two events are independent or mutually exclusive. You cannot assume either of these conditions.
• If it is not known whether A and B are independent or dependent, assume that they are dependent until you can show otherwise.
• Do not confuse two events being independent and two events being mutually exclusive. They are separate concepts.

Back to Top

Up » 3.1 Terminology » 3.2 Independent or Mutually Exclusive » 3.3 Addition and Multiplication Rules » 3.4 Contingency Tables

Lesson 1 | Lesson 2 | Lesson 3 | Lesson 4 | Lesson 5 | Lesson 6 | Lesson 7 | Lesson 8 | Lesson 9 | Lesson 10 | Lesson 11 | Lesson 12