1. Probability and Statistics
Grade 7
Copyright © Ed2Net Learning, Inc.

2. Copyright © Ed2Net Learning, Inc.
Warm Up!!
Simplify.
10C8 45
4P2 24
Copyright © Ed2Net Learning, Inc.

3. Experimental Probability
Experimental Probability is based on experimental data.
P (event) =
number of times an event occurs
number of times experiment is done
Copyright © Ed2Net Learning, Inc.

4. Experimental Probability
Example
Medical Science A medical study tests a new medicine on 3,500 people. It is effective for 3,010 people. Find the experimental probability that the medicine is effective. Then predict the number of people in a group of 6,000 for whom the medicine will be effective.
P (event) =
= 3,010/3,500 = 0.86 or 86%
number of times an event occurs
number of times experiment is done
Copyright © Ed2Net Learning, Inc.

5. Copyright © Ed2Net Learning, Inc.
Try this!!
A medicine is effective for 1,183 of 2,275 people. Find the experimental probability that the medicine is effective. Then predict the number of people in a group of 4,500 for whom the medicine will be effective.
52%; 2340 people
Copyright © Ed2Net Learning, Inc.

6. Experimental Probability
A simulation is a model used to find experimental probability.
Example: Using a Simulation
Simulate the correct guessing of true-false answers.
Toss a coin to simulate each guess. Heads represents a correct guess. The results of 50 trials are given below.
H H T T T T H H T T T H T H H H T T T H T T H T T T H T H T H H T T T H T H H H T H T H T T H T H T
Copyright © Ed2Net Learning, Inc.

7. Copyright © Ed2Net Learning, Inc.
Use Simulations
P (heads) = = =
The experimental probability of guessing correctly is .
number of heads 22 11
number of tosses 50 25 11 25
Copyright © Ed2Net Learning, Inc.

8. Copyright © Ed2Net Learning, Inc.
Your turn!!
In the previous example compare the experimental probability with the theoretical probability.
If you try the experiment 100 times, what is likely to happen to the experimental probability?
The experimental probability is less than the theoretical probability.
The experimental probability is likely to get closer to the theoretical probability of ½.
Copyright © Ed2Net Learning, Inc.

9. Experimental Probability
More than one way:
Use theoretical and experimental probabilities to find a probability for correctly guessing all the four answers on a four-question true-false quiz.
Nicole’s method:
Each guess is independent. Find the probability of one correct guess. Then find the probability of four independent correct guesses.
P (1 correct guess) =
P (4 correct guesses) =
The theoretical probability is 1 2 1 1 1 1 2 2 2 2 1 16
Copyright © Ed2Net Learning, Inc.

10. Experimental Probability
Daryl’s Method:
H T T T H T T T H H H T T T T T T T H T T H T T T H H H T H H H H T T T T T H H H T T T H T H H H T H H T H T T T T H T T H T H H H T T T H T H H H H H T T H T H H H H T H T T T T T H H H H T H H T T H T T T T H T T H H T T H H T H H T H H
Simulate the problem by tossing a coin. Let heads stand for a correct guess and tails for an incorrect guess. Use the results of 120 tosses given on the left. Separate the results into 30 groups of 4. Count the groups with 4 heads. There are two.
Copyright © Ed2Net Learning, Inc.

11. Experimental Probability
H T T T H T T T H H H T T T T T T T H T H H T T T H H H T H H H H T T T T T H H H T T T H T H H H T H H T H T T T T H T T H T H H H T T T H T H H H H H T T H T H H H H T H T T T T T H H H H T H H T T H T T T T H T T H H T T H H T H H T H H
Copyright © Ed2Net Learning, Inc.

12. Experimental Probability
Find the experimental probability.
P (event) = =
The experimental probability is
number of times an event occurs
number of times experiment is done 2 30 1 15 1 15
Copyright © Ed2Net Learning, Inc.

13. Experimental Probability
For Daryl’s simulation, the experimental probability is a little greater than the theoretical probability.
Copyright © Ed2Net Learning, Inc.

14. Copyright © Ed2Net Learning, Inc.
Choose a method
Which method would you use to solve the problem? Explain.
Answer may vary.
Copyright © Ed2Net Learning, Inc.

15. Copyright © Ed2Net Learning, Inc.
Practice
Number of Vehicles
Color
A student randomly selected 68 vehicles in a large parking lot and noted the color of each. Use the results to find the experimental probability that a vehicle chosen at random in the lot is the given color. Write the probability as a percent, to the nearest tenth of a percent.
Black 9
Blue 10
Brown 13
Green 7
Red 12
White 11
Gray 6
Copyright © Ed2Net Learning, Inc.

16. Copyright © Ed2Net Learning, Inc.
Practice
red
17.64%
black
13.2%
not black or grey
77.9 %
Copyright © Ed2Net Learning, Inc.

17. Copyright © Ed2Net Learning, Inc.
Practice
Students were surveyed about the numbers of pencils in their book bags. The table shows the results. Write each experimental probability as a fraction in simplest form.
P (one pencil)
1/2
P (two or more pencils)
3/8
No. of pencils
No. of students 1
2 or more 4 16 12
Copyright © Ed2Net Learning, Inc.

18. Copyright © Ed2Net Learning, Inc.
Practice
Two players played a number-cube game. The table
shows the results.
Find P (A wins) and P (B wins).
35.8, 64.1
A Wins
B Wins
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII
IIII II
Copyright © Ed2Net Learning, Inc.

19. Copyright © Ed2Net Learning, Inc.
Let us take a Break!
Copyright © Ed2Net Learning, Inc.

20. Copyright © Ed2Net Learning, Inc.
Assessment
An exercise is effective for 300 of 550 people. Find the experimental probability that the exercise is effective.
54.5%
While tossing a coin, head represents a correct guess.
The results of 40 trials are shown. What is the experimental probability of guessing correctly?
60 %
H H T T H T T T H T H
H T H H H H T T H T H
T H H H T H H H H T H
H H T H H T T
Copyright © Ed2Net Learning, Inc.

21. Copyright © Ed2Net Learning, Inc.
Assessment
What is the experimental probability for tossing three coins and getting three heads?
A medical experiment finds that 232 out of 1,000 patients did NOT respond to the same medication. What is the experimental probability, that a patient will respond to the medication.
76.8%
Copyright © Ed2Net Learning, Inc.

22. Copyright © Ed2Net Learning, Inc.
Assessment
A baseball manufacturer checked 250 of its baseballs and found that 8 were defective. What is the experimental probability that a baseball is NOT defective?
96.8%
What is the experimental probability that exactly three children in a family of five children will be boys? Assume that P (boy) = P (girl).
Answer may vary
Copyright © Ed2Net Learning, Inc.

23. Copyright © Ed2Net Learning, Inc.
Assessment
Use the survey data. Write the experimental probability as a fraction.
P (no pets)
9/26
P (2 or more pets)
5/26
No. of pets
No. of students 9 1 12
2 or more 5
Copyright © Ed2Net Learning, Inc.

24. Copyright © Ed2Net Learning, Inc.
Assessment
Use the survey data. Write each experimental probability as a fraction in simplest form.
P (one notebook)9/20
P (at least two notebooks)
No. of notebooks
Frequency 1 2
3 or more 9 6 4
Copyright © Ed2Net Learning, Inc.

25. Copyright © Ed2Net Learning, Inc.
Review
Experimental Probability is based on experimental data.
P (event) =
A simulation is a model used to find experimental probability
number of times an event occurs
number of times experiment is done
Copyright © Ed2Net Learning, Inc.

26. Copyright © Ed2Net Learning, Inc.
Good Job!
Remember to do the practice worksheets!!!
Copyright © Ed2Net Learning, Inc.