In this section, you will use a spinner simulator to conduct several "spins" in order to compare theoretical probabilities with experimental probabilities.

Use the "Spinner" below which has three equal-sized sections that are blue, red, and yellow.

• Spin the spinner a total of 30 times
• Record your results in the table below.

Assume that the areas of each sector of the spinner are the same.

What is the theoretical probability of the spinner landing on each color?

Check Your Answer

Since there is only one sector in each color (red, blue, and yellow), the probability of the spinner landing on each color is 1 over 3 1 3 .

Based on the theoretical probability of the spinner landing on each color, how many spins out of 30 spins should land on each color?

Hint

What is 1 over 3 1 3 of 30 spins?

Check Your Answer

There should be 10 spins of each color.

Did the actual results of the spins match the results predicted by theoretical probability? Why do you think that is the case?

Check Your Answer

Your answer may vary. Usually, actual results are close to, but not exactly like, what theoretical probability indicates should happen.

Repeat the process with the same spinner for a total of 100 spins.

Based on the theoretical probability of the spinner landing on each color, how many spins out of 100 spins should land on each color?

Hint

What is 1 over 3 1 3 of 100 spins?

Check Your Answer

There should be 33 spins of each color.

Did the actual results of the spins match the results predicted by theoretical probability? Why do you think that is the case?

Check Your Answer

Your answer may vary. Usually, the actual results are close to, but not always the same as, what is predicted by theoretical probability. This phenomenon is called the Law of Large Numbers.

Practice

Consider the spinner that is shown.

1. Calculate the theoretical probability of the spinner landing on each color.

Interactive popup. Assistance may be required.

Hint

The theoretical probability of the spinner landing on any given color is equal to the ratio:
P = Number of Spaces of Desired Color over Number of Total Spaces Number of Spaces of Desired Color Number of Total Spaces

Check Your Answer

P(red) = 2 over 8 2 8 = 1 over 4 1 4
P(purple) = 3 over 8 3 8
P(yellow) = 2 over 8 2 8 = 1 over 4 1 4
P(blue) = 1 over 8 1 8

Kazumi spun the spinner 40 times, and recorded her results in the table.

2. What is the experimental probability that the spinner will land on purple? Express your answer as a decimal.

Use the grid below to record your answer. Type your answer in the boxes in front of and behind the decimal. Click inside each box to enter the numeral that belongs in the box, and then click the bubble beneath the numeral to shade the bubble that matches the numeral. After hitting the "Submit" button, incorrect portions of your answer will be shaded gray.



3. What is the experimental probability that the spinner will land on red? Give your answer as a percent.

Interactive popup. Assistance may be required.

Hint

P = Number of Spaces of Desired Color over Number of Total Spaces Number of Actual Desired Spins Number of Total Spins Interactive popup. Assistance may be required.

Check Your Answer

30%
4. What is the difference between the experimental probability and the theoretical probability that the spinner will land on red? Give your answer as a percent.
Interactive popup. Assistance may be required.

Check Your Answer

30% - 25% = 5%