1. 10-1 Probability Warm Up Problem of the Day Lesson Presentation
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. 10-1 Probability Warm Up Write each fraction in simplest form. 1. 2.
Course 3
10-1
Probability
Warm Up
Write each fraction in simplest form. 16 20 4 5 12 36 1 3 8 1 8 39
195 1 5 64

3. 10-1 Probability Problem of the Day
Course 3
10-1
Probability
Problem of the Day
A careless reader mixed up some encyclopedia volumes on a library shelf. The Q volume is to the right of the X volume, and the C is between the X and D volumes. The Q is to the left of the G. X is to the right of C. From right to left, in what order are the volumes?
D, C, X, Q, G

4. Course 3
10-1
Probability
Learn to find the probability of an event by using the definition of probability.

5. Insert Lesson Title Here
Course 3
10-1
Probability
Insert Lesson Title Here
Vocabulary
experiment
trial
outcome
sample space
event
probability
impossible
certain

6. Course 3
10-1
Probability
An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.
Experiment Sample Space
flipping a coin heads, tails
rolling a number cube 1, 2, 3, 4, 5, 6
guessing the number of whole numbers
marbles in a jar

7. Course 3
10-1
Probability
An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen.
A probability of 0 means the event is impossible, or can never happen.
A probability of 1 means the event is certain, or has to happen.
The probabilities of all the outcomes in the sample space add up to 1.

8. 10-1 Probability Never Happens about Always
Course 3
10-1
Probability
Never Happens about Always
happens half the time happens 1 4 1 2 3 4 1
0% % % % %

9. Course 3
10-1
Probability
Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space
Give the probability for each outcome.
The basketball team has a 70% chance of winning.
The probability of winning is P(win) = 70% = 0.7. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.7 = 0.3, or 30%.

10. Course 3
10-1
Probability
Additional Example 1B: Finding Probabilities of Outcomes in a Sample Space
Give the probability for each outcome.
Three of the eight sections of the spinner are labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is
P(1) = . 3 8

11. Additional Example 1B Continued
Course 3
10-1
Probability
Additional Example 1B Continued
Three of the eight sections of the spinner are labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = . 3 8
Two of the eight sections of the spinner are labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = = . 2 8 1 4
Check The probabilities of all the outcomes must add to 1. 3 8 2 +
= 1 

12. 10-1 Probability Check It Out: Example 1A
Course 3
10-1
Probability
Check It Out: Example 1A
Give the probability for each outcome.
The polo team has a 50% chance of winning.
The probability of winning is P(win) = 50% = 0.5. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.5 = 0.5, or 50%.

13. 10-1 Probability 1 2 3 4 5 6 Check It Out: Example 1B Outcome
Course 3
10-1
Probability
Check It Out: Example 1B
Give the probability for each outcome.
Rolling a number cube.
Outcome 1 2 3 4 5 6
Probability
One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P(1) = . 1 6
One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = . 1 6

14. Check It Out: Example 1B Continued
Course 3
10-1
Probability
Check It Out: Example 1B Continued
One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = . 1 6
One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 4 is P(4) = . 1 6
One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 5 is P(5) = . 1 6

15. Check It Out: Example 1B Continued
Course 3
10-1
Probability
Check It Out: Example 1B Continued
One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 6 is P(6) = . 1 6
Check The probabilities of all the outcomes must add to 1. 1 6 +
= 1 

16. Course 3
10-1
Probability
To find the probability of an event, add the probabilities of all the outcomes included in the event.

17. Additional Example 2A: Finding Probabilities of Events
Course 3
10-1
Probability
Additional Example 2A: Finding Probabilities of Events
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
What is the probability of guessing 3 or more correct?
The event “three or more correct” consists of the outcomes 0, 1, and 2.
P(3 or more correct) = = 0.5, or 50%.

18. Additional Example 2B: Finding Probabilities of Events
Course 3
10-1
Probability
Additional Example 2B: Finding Probabilities of Events
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
What is the probability of guessing fewer than 2 correct?
The event “fewer than 2 correct” consists of the outcomes 0 and 1.
P(fewer than 2 correct) = = 0.187, or 18.7%

19. Additional Example 2C: Finding Probabilities of Events
Course 3
10-1
Probability
Additional Example 2C: Finding Probabilities of Events
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
What is the probability of passing the quiz (getting 4 or 5 correct) by guessing?
The event “passing the quiz” consists of the outcomes 4 and 5.
P(passing the quiz) = = 0.187, or 18.7%

20. 10-1 Probability Check It Out: Example 2A
Course 3
10-1
Probability
Check It Out: Example 2A
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
What is the probability of guessing 2 or more correct?
The event “two or more correct” consists of the outcomes 2, 3, 4, and 5.
P(2 or more) = = .813, or 81.3%.

21. 10-1 Probability Check It Out: Example 2B
Course 3
10-1
Probability
Check It Out: Example 2B
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
What is the probability of guessing fewer than 3 correct?
The event “fewer than 3” consists of the outcomes 0, 1, and 2.
P(fewer than 3) = = 0.5, or 50%

22. 10-1 Probability Check It Out: Example 2C
Course 3
10-1
Probability
Check It Out: Example 2C
A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.
What is the probability of passing the quiz with all 5 correct by guessing?
The event “passing the quiz” consists of the outcome 5.
P(passing the quiz) = = or 3.1%

23. Additional Example 3: Problem Solving Application
Course 3
10-1
Probability
Additional Example 3: Problem Solving Application
Six students are in a race. Ken’s probability of winning is 0.2. Lee is twice as likely to win as Ken. Roy is as likely to win as Lee. Tracy, James, and Kadeem all have the same chance of winning. Create a table of probabilities for the sample space. 14

24. Understand the Problem
Course 3
10-1
Probability
Additional Example 3 Continued 1
Understand the Problem
The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1.
List the important information:
P(Ken) = 0.2
P(Lee) = 2  P(Ken) = 2  0.2 = 0.4
P(Roy) =  P(Lee) =  0.4 = 0.1 1 4
P(Tracy) = P(James) = P(Kadeem)

25. Additional Example 3 Continued
Course 3
10-1
Probability
Additional Example 3 Continued 2
Make a Plan
You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Tracy, James, and Kadeem.
P(Ken) + P(Lee) + P(Roy) + P(Tracy) + P(James) + P(Kadeem) = 1
p p p = 1
p = 1

26. Additional Example 3 Continued
Course 3
10-1
Probability
Additional Example 3 Continued
Solve 3
p = 1
– –0.7 Subtract 0.7 from both sides.
3p = 0.3 3p 3
0.3
= Divide both sides by 3.
p = 0.1

27. Additional Example 3 Continued
Course 3
10-1
Probability
Additional Example 3 Continued
Look Back 4
Check that the probabilities add to 1.
= 1 

28. 10-1 Probability Check It Out: Example 3
Course 3
10-1
Probability
Check It Out: Example 3
Four students are in the Spelling Bee. Fred’s probability of winning is 0.6. Willa’s chances are one-third of Fred’s. Betty’s and Barrie’s chances are the same. Create a table of probabilities for the sample space.

29. Understand the Problem
Course 3
10-1
Probability
Check It Out: Example 3 Continued 1
Understand the Problem
The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1.
List the important information:
P(Fred) = 0.6
P(Willa) =  P(Fred) =  0.6 = 0.2 1 3
P(Betty) = P(Barrie)

30. Check It Out: Example 3 Continued
Course 3
10-1
Probability
Check It Out: Example 3 Continued 2
Make a Plan
You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Betty and Barrie.
P(Fred) + P(Willa) + P(Betty) + P(Barrie) = 1
p p = 1
p = 1

31. Check It Out: Example 3 Continued
Course 3
10-1
Probability
Check It Out: Example 3 Continued
Solve 3
p = 1
– –0.8 Subtract 0.8 from both sides.
2p = 0.2
p = 0.1
Outcome
Fred
Willa
Betty
Barrie
Probability
0.6
0.2
0.1

32. Check It Out: Example 3 Continued
Course 3
10-1
Probability
Check It Out: Example 3 Continued
Look Back 4
Check that the probabilities add to 1.
= 1 

33. Insert Lesson Title Here
Course 3
10-1
Probability
Insert Lesson Title Here
Lesson Quiz
Use the table to find the probability of each event.
1. 1 or 2 occurring
2. 3 not occurring
3. 2, 3, or 4 occurring
0.351
0.874
0.794