6th Grade Math Textbook, Fundamentals

Lesson 12-3 for exercise sets. &KDSWHU 

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Key Concept

Complementary Events

P(E) P(not E)  1

or

P(E) P(E)  1

Key Concept

Mutually Exclusive Events

P(A or B) P(A) P(B)

3

1

5

2

6

4

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A pair of numbered 1–6 number cubes is rolled.
Find the theoretical probability of each event.
Write each as a fraction, decimal, and percent.

1.P(multiple of 3) 2.P(odd) 3.P(not 4) 4.P(factor of 15 or 6)

5.Discuss and WriteYou and your 8 friends decide to draw straws for a prize.

There are 8 long straws and 1 short straw. Describe how the theoretical probability

of drawing the short straw changes as each friend picks a straw.

Two events, E and notE, are if

both events cannot occur at the same time. The sum of

their likelihood of occurring is 1. The complement of E

can be written as E.

There are 6 blue marbles, 4 red marbles, 7 green marbles,

and 3 yellow marbles in a bag. Find the probability of

choosing a blue marble. Then find the probability of

choosing a marble that is notblue.

complementary events

P(blue) 





 103 0.3 30%

6

20

6

6  4  7  3

number of blue marbles

total number of marbles P(not blue) ^1 P(blue)

 1 

 

0.7 70%

10

10

7

10

3

10

3

10

Two events, A and B, that have no outcomes in common

are called or.

Refer to the marbles in the bag above. Find the probability

of choosing a blue or a red marble.

P(blue or red)P(blue) P(red)



0.5 50%

Two events, A and B, that have one or more outcomes in common are

called. These events are not mutually exclusive.

A 1–6 number cube is rolled.

Are the following events mutually exclusive or overlapping?

Event A: Roll an odd number

Event B: Roll a factor of 6

Since the two events have outcomes in common,

the events are overlapping. The Venn diagram

at the right shows the overlapping outcomes.

10

20

overlapping events

mutually exclusive events disjoint events

1

2

4

20

6

20