1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. 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

3. 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%

4. Learn to estimate probability using experimental methods.

5. Vocabulary
experimental probability
simulation

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

7. Additional Example 1A: Estimating the Probability of an Event
A marble is randomly drawn out of a bag and then replaced. The table shows the results after fifty draws.
Estimate the probability of drawing a red marble.
experimental probability =
number of red marbles drawn
total number of marbles drawn =
The probability of drawing a red marble is about 0.3, or 30%.

8. Additional Example 1B: Estimating the Probability of an Event
A marble is randomly drawn out of a bag and then replaced. The table shows the results after fifty draws.
Estimate the probability of drawing a green marble.
experimental probability =
number of green marbles drawn
total number of marbles drawn =
The probability of drawing a green marble is about 0.24, or 24%.

9. Additional Example 1C: Estimating the Probability of an Event
A marble is randomly drawn out of a bag and then replaced. The table shows the results after fifty draws.
Estimate the probability of drawing a yellow marble.
experimental probability =
number of yellow marbles drawn
total number of marbles drawn =
The probability of drawing a yellow marble is about 0.46, or 46%.

10. Estimate the probability of drawing a purple ticket. Outcome Purple
Check It Out: Example 1A
A ticket is randomly drawn out of a bag and then replaced. The table shows the results after 100 draws.
Estimate the probability of drawing a purple ticket.
Outcome
Purple
Orange
Brown
Draw 55 22 23
experimental probability =
number of purple tickets drawn
total number of tickets drawn =
The probability of drawing a purple ticket is about 0.55, or 55%.

11. Estimate the probability of drawing a brown ticket. Outcome Purple
Check It Out: Example 1B
A ticket is randomly drawn out of a bag and then replaced. The table shows the results after 100 draws.
Estimate the probability of drawing a brown ticket.
Outcome
Purple
Orange
Brown
Draw 55 22 23
experimental probability =
number of brown tickets drawn
total number of tickets drawn =
The probability of drawing a brown ticket is about 0.23, or 23%.

12. Estimate the probability of drawing a blue ticket. Outcome Red Blue
Check It Out: Example 1C
A ticket is randomly drawn out of a bag and then replaced. The table shows the results after 1000 draws.
Estimate the probability of drawing a blue ticket.
Outcome
Red
Blue
Pink
Draw
285
112
603
experimental probability =
number of blue tickets drawn
total number of tickets drawn =
The probability of drawing a blue ticket is about 0.112, or 11.2%.

13. Additional Example 2: Sports Application
Which team is most likely to win their next game? Justify your answer.

14. Additional Example 2 Continued
probability for a Huskies win =
138 79
 0.572
150
probability for a Cougars win = 85
 0.567
146
probability for a Knights win = 90
 0.616
The Knights are most likely to win their next game.

15. Outcome Wins Games Tigers 65 152 Longhorns 78 138 Dolphins 86 170
Check It Out: Example 2
Which team is most likely to win their next game? Justify your answer.
Outcome
Wins
Games
Tigers 65
152
Longhorns 78
138
Dolphins 86
170

16. Check It Out: Example 2 Continued
probability for a Tigers win =
152 65
 0.428
138
probability for a Longhorns win = 78
 0.565
170
probability for a Dolphins win = 86
 0.506
The Longhorns are most likely to win their next game.

17. Additional Example 3: Using a Number Cube for Simulation
One out of every 3 students will win a prize at a festival. Simulate by using a number cube, and estimate the probability that from 8 randomly chosen students, at least 2 will win a prize.
Step 1: Since 1 out of every 3 students will win a prize, let the numbers 1 and 2 represent a student that won a prize and the numbers 3 through 6 represent a student that did not win a prize.

18. Additional Example 3 Continued
Step 2: Because you want to know the probability that from 8 randomly chosen students, at least 2 will win a prize, roll the number cube 8 times, which represents one trial.

19. Additional Example 3 Continued
Step 3: Complete Step 2 until you have 10 trials.
Trial
Rolls
At least 2 students won? 1
YES 2 3 4 5 no 6 7 8 9 No 10

20. Additional Example 3 Continued
In 8 out of the 10 trials, at least 2 students from 8 randomly chosen students won a prize, so the estimated probability is about 80%.

21. Check It Out: Example 3
One out of every 2 students will win a prize at a festival. Simulate by using a number cube, and estimate the probability that from 6 randomly chosen students, at least 2 will win a prize.
Step 1: Since 1 out of every 2 students will win a prize, let the numbers 1 through 3 represent a student that won a prize and the numbers 4 through 6 represent a student that did not win a prize.

22. Check It Out: Example 3 Continued
Step 2: Because you want to know the probability that from 6 randomly chosen students, at least 2 will win a prize, roll the number cube 6 times, which represents one trial.

23. Check It Out: Example 3 Continued
Step 3: Complete Step 2 until you have 10 trials.
Trial
Rolls
At least 2 students won? 1
YES 2 3 4 5 no 6 7 8 9 10

24. Check It Out: Example 3 Continued
In 8 out of the 10 trials, at least 2 students from 6 randomly chosen students won a prize, so the estimated probability is about 80%.

25. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 25

26. Lesson Quiz: Part I
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%

27. Lesson Quiz: Part II
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%

28. Lesson Quiz for Student Response Systems
1. An experiment was carried out throwing a spoon. The number of times it landed facing up was recorded. When the spoon was thrown 125 times, it landed facing up 55 times. Estimate the probability that the spoon lands facing up.
A or 44%
B or 55%
C. 0.7 or 70%
D or 85% 28

29. Lesson Quiz for Student Response Systems
2. A deck of playing cards was shuffled and after each shuffle the suit of the top card was recorded. This was repeated 600 times out of which a diamond emerged as the top card 158 times. Estimate the probability of getting a diamond on the top in the next shuffle.
A or 16%
B or 26%
C or 52%
D or 74% 29

30. Lesson Quiz for Student Response Systems
3. Juan conducted a survey of 550 employees about their favorite hobby. Of these, 169 employees chose reading and 233 employees chose swimming. Compare the probability of an employee’s choosing reading to an employee’s choosing swimming.
A. about 32% to about 42%
B. about 32% to about 44%
C. about 31% to about 44%
D. about 31% to about 42% 30