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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math ยท Unit 7

Theory and
Experiment

Compare a theoretical probability with an experimental probability.

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Key Ideas Easy Medium Hard
What to Remember

Theory and experiment

Theory is what should happen. An experiment is what did happen.

They are not always equal.

The gap

The gap often shrinks as trials grow, but not on every added trial.

Level 1

Easy

The experiment matches the theory

Example
The theoretical probability of heads (1 favorable outcome out of 2) is 1 out of 2. An experiment got 5 successes in 10 trials. How far is the experimental probability from the theoretical probability?

theoretical probability = 12

12

experimental probability = 510

12

Subtract to compare them.

0

Answer: 0

1
The theoretical probability of tails (1 favorable outcome out of 2) is 1 out of 2. An experiment got 4 successes in 8 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 12

12

experimental probability = 48

12

Subtract to compare them.

0

Answer: 0

2
The theoretical probability of an even roll (1 favorable outcome out of 2) is 1 out of 2. An experiment got 6 successes in 12 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 12

12

experimental probability = 612

12

Subtract to compare them.

0

Answer: 0

3
The theoretical probability of rolling a 3 (1 favorable outcome out of 6) is 1 out of 6. An experiment got 2 successes in 12 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 16

16

experimental probability = 212

16

Subtract to compare them.

0

Answer: 0

4
The theoretical probability of rolling a 1 (1 favorable outcome out of 6) is 1 out of 6. An experiment got 3 successes in 18 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 16

16

experimental probability = 318

16

Subtract to compare them.

0

Answer: 0

5
The theoretical probability of a red marble (1 favorable outcome out of 4) is 1 out of 4. An experiment got 2 successes in 8 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 14

14

experimental probability = 28

14

Subtract to compare them.

0

Answer: 0

6
The theoretical probability of a blue marble (1 favorable outcome out of 4) is 1 out of 4. An experiment got 3 successes in 12 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 14

14

experimental probability = 312

14

Subtract to compare them.

0

Answer: 0

7
The theoretical probability of a green spin (1 favorable outcome out of 5) is 1 out of 5. An experiment got 2 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 15

15

experimental probability = 210

15

Subtract to compare them.

0

Answer: 0

8
The theoretical probability of a purple spin (2 favorable outcomes out of 5) is 2 out of 5. An experiment got 4 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 25

25

experimental probability = 410

25

Subtract to compare them.

0

Answer: 0

9
The theoretical probability of a shaded spin (3 favorable outcomes out of 4) is 3 out of 4. An experiment got 6 successes in 8 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 34

34

experimental probability = 68

34

Subtract to compare them.

0

Answer: 0

10
The theoretical probability of a winning ticket (1 favorable outcome out of 10) is 1 out of 10. An experiment got 2 successes in 20 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 110

110

experimental probability = 220

110

Subtract to compare them.

0

Answer: 0

Level 2

Medium

A small gap

Example
The theoretical probability of heads (1 favorable outcome out of 2, and 6 successes in 10 trials) is 1 out of 2. An experiment got 6 successes in 10 trials. How far is the experimental probability from the theoretical probability?

theoretical probability = 12

12

experimental probability = 610

35

Subtract to compare them.

110

Answer: 110

1
The theoretical probability of tails (1 favorable outcome out of 2, and 4 successes in 10 trials) is 1 out of 2. An experiment got 4 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 12

12

experimental probability = 410

25

Subtract to compare them.

110

Answer: 110

2
The theoretical probability of rolling a 4 (1 favorable outcome out of 6, and 2 successes in 6 trials) is 1 out of 6. An experiment got 2 successes in 6 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 16

16

experimental probability = 26

13

Subtract to compare them.

16

Answer: 16

3
The theoretical probability of a red marble (1 favorable outcome out of 4, and 3 successes in 10 trials) is 1 out of 4. An experiment got 3 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 14

14

experimental probability = 310

310

Subtract to compare them.

120

Answer: 120

4
The theoretical probability of a blue spin (1 favorable outcome out of 5, and 3 successes in 10 trials) is 1 out of 5. An experiment got 3 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 15

15

experimental probability = 310

310

Subtract to compare them.

110

Answer: 110

5
The theoretical probability of a green card (1 favorable outcome out of 3, and 4 successes in 10 trials) is 1 out of 3. An experiment got 4 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 13

13

experimental probability = 410

25

Subtract to compare them.

115

Answer: 115

6
The theoretical probability of a purple marble (2 favorable outcomes out of 5, and 5 successes in 10 trials) is 2 out of 5. An experiment got 5 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 25

25

experimental probability = 510

12

Subtract to compare them.

110

Answer: 110

7
The theoretical probability of a shaded section (3 favorable outcomes out of 4, and 8 successes in 10 trials) is 3 out of 4. An experiment got 8 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 34

34

experimental probability = 810

45

Subtract to compare them.

120

Answer: 120

8
The theoretical probability of an orange tile (3 favorable outcomes out of 5, and 7 successes in 10 trials) is 3 out of 5. An experiment got 7 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 35

35

experimental probability = 710

710

Subtract to compare them.

110

Answer: 110

9
The theoretical probability of a coin landing heads (1 favorable outcome out of 2, and 3 successes in 8 trials) is 1 out of 2. An experiment got 3 successes in 8 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 12

12

experimental probability = 38

38

Subtract to compare them.

18

Answer: 18

10
The theoretical probability of a winning spin (2 favorable outcomes out of 3, and 7 successes in 10 trials) is 2 out of 3. An experiment got 7 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 23

23

experimental probability = 710

710

Subtract to compare them.

130

Answer: 130

Level 3

Hard

Compare the two probabilities

Example
The theoretical probability of heads across two experiments (3 successes in 10 trials and 49 successes in 100 trials) is 1 out of 2. One experiment had 3 successes in 10 trials. A larger experiment had 49 successes in 100 trials. Which experiment is closer to the theoretical probability?

theoretical probability = 12

small experiment = 310

distance = 15

larger experiment = 49100

distance = 1100

The larger experiment is closer this time.

More trials tend to move the experimental probability toward the theoretical probability. A bigger sample is not closer on every single try.

Answer: the experiment with 100 trials

1
The theoretical probability of heads in a short test (1 favorable outcome out of 2, and 9 successes in 10 trials) is 1 out of 2. An experiment got 9 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 12

12

experimental probability = 910

910

Subtract to compare them.

25

Answer: 25

2
The theoretical probability of rolling a 2 (1 favorable outcome out of 6, and 5 successes in 12 trials) is 1 out of 6. An experiment got 5 successes in 12 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 16

16

experimental probability = 512

512

Subtract to compare them.

14

Answer: 14

3
The theoretical probability of a red marble in a bag (1 favorable outcome out of 4, and 7 successes in 12 trials) is 1 out of 4. An experiment got 7 successes in 12 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 14

14

experimental probability = 712

712

Subtract to compare them.

13

Answer: 13

4
The theoretical probability of a blue card (2 favorable outcomes out of 5, and 8 successes in 10 trials) is 2 out of 5. An experiment got 8 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 25

25

experimental probability = 810

45

Subtract to compare them.

25

Answer: 25

5
The theoretical probability of a shaded spinner (3 favorable outcomes out of 8, and 7 successes in 10 trials) is 3 out of 8. An experiment got 7 successes in 10 trials. How far is the experimental probability from the theoretical probability?
Show Answer

theoretical probability = 38

38

experimental probability = 710

710

Subtract to compare them.

1340

Answer: 1340

6
The theoretical probability of tails in two experiments (6 successes in 10 trials and 55 successes in 100 trials) is 1 out of 2. One experiment had 6 successes in 10 trials. A larger experiment had 55 successes in 100 trials. Which experiment is closer to the theoretical probability?
Show Answer

theoretical probability = 12

small experiment = 610

distance = 110

larger experiment = 55100

distance = 120

The larger experiment is closer this time.

More trials tend to move the experimental probability toward the theoretical probability. A bigger sample is not closer on every single try.

Answer: the experiment with 100 trials

7
The theoretical probability of drawing a heart in two experiments (3 successes in 8 trials and 28 successes in 100 trials) is 1 out of 4. One experiment had 3 successes in 8 trials. A larger experiment had 28 successes in 100 trials. Which experiment is closer to the theoretical probability?
Show Answer

theoretical probability = 14

small experiment = 38

distance = 18

larger experiment = 28100

distance = 3100

The larger experiment is closer this time.

More trials tend to move the experimental probability toward the theoretical probability. A bigger sample is not closer on every single try.

Answer: the experiment with 100 trials

8
The theoretical probability of spinning yellow in two experiments (3 successes in 10 trials and 22 successes in 100 trials) is 1 out of 5. One experiment had 3 successes in 10 trials. A larger experiment had 22 successes in 100 trials. Which experiment is closer to the theoretical probability?
Show Answer

theoretical probability = 15

small experiment = 310

distance = 110

larger experiment = 22100

distance = 150

The larger experiment is closer this time.

More trials tend to move the experimental probability toward the theoretical probability. A bigger sample is not closer on every single try.

Answer: the experiment with 100 trials

9
The theoretical probability of rolling a multiple of 3 in two experiments (2 successes in 9 trials and 30 successes in 90 trials) is 1 out of 3. One experiment had 2 successes in 9 trials. A larger experiment had 30 successes in 90 trials. Which experiment is closer to the theoretical probability?
Show Answer

theoretical probability = 13

small experiment = 29

distance = 19

larger experiment = 3090

distance = 0

The larger experiment is closer this time.

More trials tend to move the experimental probability toward the theoretical probability. A bigger sample is not closer on every single try.

Answer: the experiment with 90 trials

10
The theoretical probability of drawing a green marble in two experiments (4 successes in 9 trials and 60 successes in 90 trials) is 2 out of 3. One experiment had 4 successes in 9 trials. A larger experiment had 60 successes in 90 trials. Which experiment is closer to the theoretical probability?
Show Answer

theoretical probability = 23

small experiment = 49

distance = 29

larger experiment = 6090

distance = 0

The larger experiment is closer this time.

More trials tend to move the experimental probability toward the theoretical probability. A bigger sample is not closer on every single try.

Answer: the experiment with 90 trials

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