Possible Points: 100 Points Earned:
Group Activity 4: Interactive Probability Spinner
Group Members:
(Only one completed activity sheet per group will be graded. The group grade will be the number of points each individual group member earns for this activity.)
The following activity involves computing probabilities using a spinner. Directions for using the spinner are on the last page of the activity. Students will need a pencil and a paper clip to complete this activity.
PART I – Probabilities involving a single spinner
- If you spin the spinner one time, what is the theoretical probability of the spinner landing on red? Write your answer as a fraction.
- Spin the spinner a total of 20 times (you should divide the spinning up among your group members), and record the total number of times the spinner lands on each color. If the spinner lands on a line, spin again.
Your data: RED BLUE YELLOW BLACK
- Based on your data, what is the empirical probability of landing on red? Write your answer as a fraction reduced to lowest terms.
- Did your empirical probability of landing on red equal the theoretical probability of landing on red? If not, explain the difference.
- If you increased the number of spins, what would you expect to see happen in terms of the empirical probability of landing on red compared to the theoretical probability of landing on red? What law supports your answer?
PART II – Probabilities involving two spinners
Imagine now, that instead of using one spinner, you spin two spinners simultaneously, and then mix the two colors together. If you spin the same color on both spinners, the resulting color is the same (for example, red + red = red), but if you spin one primary color (red, blue, or yellow) on the first spinner and a different primary color on the second spinner, the colors combine to give you a different color (for example, red + yellow = orange). Also, for the purposes of this experiment black + any color = black. The sample space, therefore, is:
C = {red, yellow, blue, black, orange, green, and purple}
Complete the tree diagram below to find all the possible color combinations of the two spinners. The first branch of the tree diagram has been completed.
For each resulting color, use the tree diagram to find the corresponding theoretical probabilities. Fill in the theoretical probabilities in the table below as fractions reduced to lowest terms.
| Resulting Color | Theoretical Probability |
| Red | |
| Yellow | |
| Blue | |
| Black | |
| Orange | |
| Green | |
| Purple |
- What is the theoretical probability of getting red as the resulting color?
- Using the multiplication property of probability show how you could have used this property to obtain the same answer as your answer to question 6. (See pages 342-343 in textbook)
- Which color are you most likely to get? What is the theoretical probability of getting this color?
- What is the theoretical probability of getting a primary color?
- What is the theoretical probability of not getting a primary color?
- What is the theoretical probability of getting orange, green, or purple?
- What are the odds in favor of getting a primary color? What are the odds in favor of getting a result of black?
PART III – Expectation
- Suppose you want to play a game of chance involving the resulting color probabilities found in Part II. It costs $1 up front to play. If the resulting color is black, you get $0.25. If the resulting color is a primary color, you get $2.00. If the resulting color is orange, green, or purple, you get $0.50. What is the expected value of this game if you play it one time? (Hint: Use the probabilities you obtained in questions 8, 9, and 11).
- What is the expected value of the game if you played the game 20 times?
- Using two spinners, spin the two spinners simultaneously 20 times and record the number of times you get the resulting colors below. (For the purposes of this experiment, “OTHER” refers to the total number of times the resulting color is orange, green, or purple).
Your data: PRIMARY COLOR BLACK OTHER
- Use the results of your 20 spins to determine how much money you would have actually won (or lost) if you played the game as described. Remember, you have to pay $1 each time you play.
