Pre-Test		Post-Test
Q&A	Probability

Instruction 7-2

Probability of Events | Relationships Between Events | Geometric Probability | Summary

Two events A and B chosen from the same sample space are called mutually exclusive or disjoint if there is no common outcome for A and B. This property is denoted by . That is, the intersection of the sets A and B is empty.

For example, the events {1, 3} and {2, 4, 6} are mutually exclusive events in the rolling a die. This concept can be illustrated by the figure below, in which the rectangle considered as the sample space of an experiment, and the circles A and B display the two disjoint events:

For two given disjoint events A and B, if A is the set of outcomes of the event A and B is the set of the outcomes of the event B, then the probability of observing a result that is in both A and B is zero. This can be denoted by the expression below:

Probability of Union of Two Events
If A and B are two events form the same sample space, then the probability of occurring A or B is denoted by  and is defined as follows:

If A and B are mutually exclusive events, then

Now let's do Practice Exercise 7-2-a

Probability of Intersection of Two Events
If in a sample space, the events A and B have some common elements, then these elements are denoted by the set (AI B), and the probability of such an event is calculated using the formula below:

For example, assume that the rectangle below illustrates the sample space of an experiment in which a coin and a die tossed together. Consider the following events:

Event A: Set of all outcomes paired by a heads and an even number
Event B: Set of all outcomes paired by a heads and a number less than 5 and greater than 2.

Then as shown in the figure, these sets have one common element which is displayed in the intersection part of the sets A and B.

Complement of an Event
If all the elements of a sample space collected in two different sets such that they have no common elements, then these events are called complementary events, and each complements the other. Thus, the union of two complementary events is the same as the sample space and their intersection is .

If the event A is in a sample space S, the complement of A, those members of S that are not in A denoted by A’ or A^c.

Properties of Complement Event

1. Probability of occurring an event A or its complement is 1
2. If A’ is the complement of the event A, then P(A’) = 1 – P(A)

Practice 3. Why an event with the probability is highly possible to occur?

Answer
Since is extremely closer to 1.

Video Instruction
*Availability of You Tube video links may vary. eTAP has no control of these materials.

• Mutually Exclusive Vs Independent Events [3:38]

• Probability of the Intersection of 2 Events [10:19]

• Probability of Complement of an Event [5:05]

for Students, Parents and Teachers

Now let's do Practice Exercise7-2-b (top).

Next Page: Geometric Probability (top)