Theoretical vs Experimental Probability

Experimental probability: Probability based on a collection of data.

•Will have a table of results or data from the experiment(s)!

What is the difference between theoretical probability and experimental probability?

• Theoretical probability shows what should happen in an experiment.

• Experimental probability shows what actually happened.

1. P (heads) =________

2. P (tails) = ________

Jim tossed a coin 35 times. He recorded whether the coin landed on heads or tails. Use the results in the table to find each experimental probability.

HEADS TAILS

llll llll llllllll

llll llll llll

7

3

7

4

35

1535

20

3.What is the theoretical probability of throwing heads?

4. tails?

2

1

2

1

5. What is the difference between the experimental probability of throwing heads and the theoretical probability of throwing heads? (write answer as a percent rounded to the nearest whole percent)

2

1

7

4

14

1

14

7

14

8

Experimental - theoretical

This is about 7%

6. What is the difference between the experimental probability of throwing tails and the theoretical probability of throwing tails? (write answer as a percent rounded to the nearest whole percent)

7

3

2

1

14

1

14

6

14

7

Theoretical - Experimental

This is about 7%

Mrs. Smith has a bag that contains 6 red Lifesavers, 5 yellow Lifesavers, 8 orange Lifesavers and 9 white Lifesavers. She has another bag that contains 3 Butterfingers, 6 Snickers, and 4 Hershey Bars. You are a student that is being rewarded for good behavior so you get to draw a piece of candy from each bag. Find the following probabilities.

Lifesavers

6-red

5 yellow

8 orange

9 white

Candy Bars

3-Butterfingers

6 Snickers

4 Hershey Bars

Lifesavers

6-red

5 yellow

8 orange

9 white

Candy Bars

3-Butterfingers

6 Snickers

4 Hershey Bars

7.P(yellow Lifesaver, a Snickers)

8.P(red or orange Lifesaver, a Hershey Bar)

9. P(no white lifesaver, a Butterfinger)

13

4

28

86

%813

6

28

5

13

4

28

14

182

15

57

36416%

13

3

28

19

13

3

28

658

%1513

2

David rolled a number cube, with the numbers 1-6 on it. He recorded the results in the table below.

Number Outcomes

1 IIII2 III3 IIII4 IIII I5 II6 I

Find the THEORETICAL probabilites:

10) P(4) = ______________

11) P(odd number) = __________

12) P(2 or 5) = __________

13) P(a factor of 3) = _________

14) What is the difference between the experimental probability of rolling a 2 or 5, and the theoretical probability of rolling a 2 or 5?

1/6½

1/3

1/3

1/3 – 1/4 = 1/12