1. Pledge & Moment of Silence

2. Pre-Algebra HOMEWORK
Page 449 #1-8 & Page 453 #1-6

3. Our Learning Goal
Students will be able to find theoretical probabilities, including dependent and independent events; estimate probabilities using experiments and simulations; use The Fundamental Counting Principle, permutations, and combinations; and convert between probability and odds of a specified outcome.

4. Our Learning Goal Assignments
Learn to find he probability of an event by using the definition of probability (9-1)
Learn to estimate probability using experimental methods (9-2)

5. Learning Goal Scale Students are able to determine & construct fractions, decimals, & percents:4 3 2 1
Clear understanding their relationships
Able to solve for the unknown
Understands how to solve for increase & decrease
Calculating solving sales tax/total cost contextual problems
Computing simple interest
Understands their relationships
Some solving for the unknown
Difficulty solving for increase & decrease
Difficulty solving for the unknown
Some understanding their relationships
Even with help, no understanding or skill demonstrated

6. Student Learning Goal Chart

7. 9-1 Probability Warm Up Problem of the Day Lesson Presentation
Pre-Algebra

8. FAST TRACK!
9-1 and 9-2

9. Today’s Learning Goal Assignment
Learn to find the probability of an event by using the definition of probability.

10. 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

11. 9-2 Experimental Probability
Today’s Learning Goal Assignment
Learn to estimate probability using experimental methods.

12. 9-2 Experimental Probability
Lesson Quiz: Part 1
1. Of 425, 234 seniors were enrolled in a math course. Estimate the probability that a randomly selected senior is enrolled in a math course.
2. Mason made a hit 34 out of his last 125 times at bat. Estimate the probability that he will make a hit his next time at bat.
0.55, or 55%
0.27, or 27%

13. 9-2 Experimental Probability
Lesson Quiz: Part 2
3. Christina polled 176 students about their favorite ice cream flavor. 63 students’ favorite flavor is vanilla and 40 students’ favorite flavor is strawberry. Compare the probability of a student’s liking vanilla to a student’s liking strawberry.
about 36% to about 23%

14. 9-1 Probability Warm Up Write each fraction in simplest form. 1. 2.
Pre-Algebra
9-1
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

15. 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

16. Vocabulary experiment trial outcome sample space event probability
impossible
certain

17. An experiment is an activity in which results are observed
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
jelly beans in a jar

18. An event is any set of one or more outcomes
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.

19. Never Happens about Always
happens half the time happens 1 4 1 2 3 4 1
0% % % % %

20. A. The basketball team has a 70% chance of winning.
Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space
Give the probability for each outcome.
A. 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%.

21. A. The polo team has a 50% chance of winning.
Try This: Example 1A
Give the probability for each outcome.
A. 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%.

22. Additional Example 1B: Finding Probabilities of Outcomes in a Sample Space
Give the probability for each outcome. B.
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

23. 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 

24. B. Rolling a number cube. 1 2 3 4 5 6 Try This: Example 1B Outcome
Give the probability for each outcome.
B. 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 1 is P(2) = . 1 6

25. Try This: 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 1 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 1 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 1 is P(5) = . 1 6

26. Try This: 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 1 is P(6) = . 1 6
Check The probabilities of all the outcomes must add to 1. 1 6 +
= 1 

27. To find the probability of an event, add the probabilities of all the outcomes included in the event.

28. 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.
A. What is the probability of not guessing 3 or more correct?
The event “not three or more correct” consists of the outcomes 0, 1, and 2.
P(not 3 or more) = = 0.5, or 50%.

29. Try This: 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.
A. What is the probability of guessing 3 or more correct?
The event “three or more correct” consists of the outcomes 3, 4, and 5.
P(3 or more) = = 0.5, or 50%.

30. 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.
B. What is the probability of guessing between 2 and 5?
The event “between 2 and 5” consists of the outcomes 3 and 4.
P(between 2 and 5) = = 0.469, or 46.9%

31. Try This: 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.
B. 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%

32. 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.
C. What is the probability of guessing an even number of questions correctly (not counting zero)?
The event “even number correct” consists of the outcomes 2 and 4.
P(even number correct) = = 0.469, or 46.9%

33. Try This: 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.
C. 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%

34. 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

35. Understand the Problem
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)

36. Additional Example 3 Continued2
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

37. 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

38. Additional Example 3 Continued
Look Back 4
Check that the probabilities add to 1.
= 1 

39. Try This: 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.

40. Understand the Problem
Try This: 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)

41. Try This: Example 3 Continued2
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

42. Try This: 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

43. Try This: Example 3 Continued
Look Back 4
Check that the probabilities add to 1.
= 1 

44. 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

45. Experimental Probability
9-2
Experimental Probability
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

46. Experimental Probability
Pre-Algebra
9-2
Experimental Probability
Warm Up
Use the table to find the probability of each event.
1. A or B occurring
2. C not occurring
3. A, D, or E occurring
0.494
0.742
0.588

47. Problem of the Day
A spinner has 4 colors: red, blue, yellow, and green. The green and yellow sections are equal in size. If the probability of not spinning red or blue is 40%, what is the probability of spinning green?
20%

48. Today’s Learning Goal Assignment
Learn to estimate probability using experimental methods.

49. Vocabulary
experimental probability

50. In experimental probability, the likelihood of an event is estimated by repeating an experiment many times and observing the number of times the event happens. That number is divided by the total number of trials. The more the experiment is repeated, the more accurate the estimate is likely to be.
number of times the event occurs
total number of trials
probability 

51. Additional Example 1A: Estimating the Probability of an Event
A. The table shows the results of 500 spins of a spinner. Estimate the probability of the spinner landing on 2.
number of spins that landed on 2
total number of spins =
500
186
probability 
The probability of landing on 2 is about 0.372, or 37.2%.

52. Try This: Example 1A
A. Jeff tosses a quarter 1000 times and finds that it lands heads 523 times. What is the probability that the next toss will land heads? Tails?
1000
523
P(heads) =
= 0.523
P(heads) + P(tails) = 1 The probabilities must equal 1.
P(tails) = 1
P(tails) = 0.477

53. Additional Example 1B: Estimating the Probability of an Event
B. A customs officer at the New York–Canada border noticed that of the 60 cars that he saw, 28 had New York license plates, 21 had Canadian license plates, and 11 had other license plates. Estimate the probability that a car will have Canadian license plates.
number of Canadian license plates
total number of license plates 60 =
probability 
= 0.35
The probability that a car will have Canadian license plates is about 0.35, or 35%.

54. Try This: Example 1B
B. Josie sells TVs. On Monday she sold 13 plasma displays and 37 tube TVs. What is the probability that the first TV sold on Tuesday will be a plasma display? A tube TV?
number of plasma displays
total number of TVs = 13 =
1350
probability ≈
P(plasma) = 0.26
P(plasma) + P(tube) = 1
P(tube) = 1
P(tube) = 0.74

55. Additional Example 2: Application
Use the table to compare the probability that the Huskies will win their next game with the probability that the Knights will win their next game.

56. Additional Example 2 Continued
number of wins
total number of games
probability 
probability for a Huskies win 
138 79
 0.572
146
probability for a Knights win  90
 0.616
The Knights are more likely to win their next game than the Huskies.

57. Try This: Example 2
Use the table to compare the probability that the Huskies will win their next game with the probability that the Cougars will win their next game.

58. Try This: Example 2 Continued
number of wins
total number of games
probability 
probability for a Huskies win 
138 79
 0.572
150
probability for a Cougars win  85
 0.567
The Huskies are more likely to win their next game than the Cougars.

59. Lesson Quiz: Part 1
1. Of 425, 234 seniors were enrolled in a math course. Estimate the probability that a randomly selected senior is enrolled in a math course.
2. Mason made a hit 34 out of his last 125 times at bat. Estimate the probability that he will make a hit his next time at bat.
0.55, or 55%
0.27, or 27%

60. Lesson Quiz: Part 2
3. Christina polled 176 students about their favorite ice cream flavor. 63 students’ favorite flavor is vanilla and 40 students’ favorite flavor is strawberry. Compare the probability of a student’s liking vanilla to a student’s liking strawberry.
about 36% to about 23%