1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
A bag contains 18 marbles; 4 are green, 8 are red, and 6 are yellow. Find the probability of each event when a marble is chosen at random.
1. yellow 2. red
3. green 4. blue
5. not red 1 3 4 9 2 9 5 9

3. California
Standards
SDAP3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.
Also covered: SDAP3.1

4. Vocabulary
disjoint events

5. On a game show, the letters in the word Hollywood are printed on cards and shuffled. A contestant will win a trip to Hollywood if the first card she chooses is printed with an O or an L.
Choosing an O or an L on the first card is an example of a set of disjoint events. Disjoint events cannot occur in the same trial of an experiment.

6. P(A or B) = P(A) + P(B) Probability of Two Disjoint Events
Probability of either event
Probability of one event
Probability of other event
Disjoint events are sometimes called mutually exclusive events.
Reading Math

7. Additional Example 1: Identifying Disjoint Events
Determine whether each set of events is disjoint. Explain.
A. choosing a dog or a poodle from the animals at an animal shelter
The event is not disjoint. A poodle is a type of dog, so it is possible to choose an animal that is both a dog and a poodle.
B. choosing a fish or a snake from the animals at a pet store
The event is disjoint. Fish and snakes are different types of animals, so you cannot choose an animal that is both a fish and a snake.

8. Additional Example 2: Finding the Probability of Disjoint Events
Find the probability of each set of disjoint events.
A. choosing an A or an E from the letters in the word mathematics 2 11
P(E) = 1 11
P(A) =
Add the probabilities of the individual events.
P(A or E) = P(A) + P(E) 2 11 1 11 3 11
= = 3 11
The probability of choosing an A or an E is .

9. Additional Example 3: Recreation Application
Sharon rolls two number cubes. What is the probability that the sum of the numbers shown on the cubes is 2 or 8?
Step 1 Use a grid to find the sample space. 1 2 3 4 5 6 7 8 9 10 11 12
First Roll
Second Roll
The grid shows all possible sums.
There are 36 equally likely outcomes in the sample space.

10. Additional Example 3 Continued
Sharon rolls two number cubes. What is the probability that the sum of the numbers shown on the cubes is 2 or 8?
Step 2 Find the probability of the set of disjoint events. 1 36
P(sum of 8) = 5 36
P(sum of 2) =
P(sum of 2 or sum of 8) = P(sum of 2) + P(sum of 8) 1 36 5 36 6 36 1 6
= = = 1 6
The probability that the sum of the cubes is 2 or 8 is .

11. Determine whether each set of events is disjoint. Explain.
Check It Out! Example 1
Determine whether each set of events is disjoint. Explain.
A. choosing a bowl of soup or a bowl of chicken noodle soup from the cafeteria
The event is not disjoint. Chicken noodle is a type of soup, so it is possible to choose a bowl of chicken noodle soup and soup.
B. choosing a bowl of chicken noodle soup or broccoli cheese soup
The event is disjoint. Chicken noodle and broccoli cheese are different types of soups, so you cannot choose a soup that is both chicken noodle and broccoli cheese.

12. Find the probability of each set of disjoint events.
Check It Out! Example 2
Find the probability of each set of disjoint events.
A. choosing an I or an E from the letters in the word centimeter 1 10
P(E) = 3 10
P(I) =
Add the probabilities of the individual events.
P(I or E) = P(I) + P(E) 1 10 3 10 4 10 2 5
= = = 2 5
The probability of choosing an I or an E is .

13. Find the probability of each set of disjoint events.
Check It Out! Example 2
Find the probability of each set of disjoint events.
B. spinning a 2 or a 4 on a spinner with eight equal sectors numbered 1-6 1 6
P(4) = 1 6
P(2) =
Add the probabilities of the individual events.
P(2 or 4) = P(2) + P(4) 1 6 1 6 2 6 1 3
= = = 1 3
The probability of choosing a 2 or a 4 is .

14. Step 1 Use a grid to find the sample space.
Check It Out! Example 3
Sun Li rolls two number cubes. What is the probability that the sum of the numbers shown on the cubes is 3 or 4?
Step 1 Use a grid to find the sample space. 1 2 3 4 5 6 7 8 9 10 11 12
First Roll
Second Roll
The grid shows all possible sums.
There are 36 equally likely outcomes in the sample space.

15. Check It Out! Example 3 Continued
Sun Li rolls two number cubes. What is the probability that the sum of the numbers shown on the cubes is 3 or 4?
Step 2 Find the probability of the set of disjoint events. 2 36
P(sum of 4) = 3 36
P(sum of 3) =
P(sum of 3 or sum of 4) = P(sum of 3) + P(sum of 4) 2 36 3 36 5 36
= = 5 36
The probability that the sum of the cubes is 3 or 4 is .

16. Lesson Quiz: Part I
1. Determine whether choosing a fiction book or a nonfiction book is a set of disjoint events. Explain.
Find the probability of each set of disjoint events.
2. Choosing an O or an E from the letters in outcome
3. Rolling an odd number or a 6 on a number cube
Disjoint; you cannot choose a book that is both fiction and nonfiction.
3 7
2 3

17. Lesson Quiz: Part II
4. David rolls two number cubes at the same time. If the product of the numbers rolled is 25 or 30, he will win the game. Use a grid to find the sample space. The find the probability that David will win the game.
1 12