Name ______
Lucky Number
Before Opening the Lucky Number File
Scenario:
Suppose you are playing a game with three spinners. Each spinner is labeled with the numbers 0 – 9. Each of the number sections on the spinners are the same size. By spinning all three spinners at the same time, you get a three-digit number. For example, if your results were the ones pictured above, your three-digit number would be 915. The object of the game is to guess the three-digit number before spinning the spinners.
1. Make a list of 10 three-digit numbers that have the best chance of coming up in the spinner game.
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2. Look over the numbers that you just listed. What strategy or rationale did you use in choosing these numbers?
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3. If you were to select one of the numbers that you listed and play the spinner game 1500 times, how many points do you think that you would get? ______How did you arrive at that answer?
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Before Running Simulations
Open up the Lucky Number excel file. Do not press anything on your keyboard yet. On the left are simulations representing 1500 rounds of the spinner game. In the center are listed results for two particular guesses: the three digit numbers 123 and 333, as well as results for a number that you are allowed to guess for yourself. On the right is a bar graph of these same results.
4. Did you choose the numbers 123 and 333 when you listed your “best guesses” in problem number one? Why or why not?
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5. Do you consider 123 and 333 to be truly “lucky numbers”? That is, would you feel comfortable guessing them in the spinner game? ______Why or why not?
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Running Simulations
Press F9 several times to get a feel for how the simulation, the results, and the graph work together.
6. Try each of the ten numbers that you listed in question #1 in the Your Choice spot. Try each number one time and record the results below:
Your 10 “Lucky” Numbers Frequency in 1500 trials
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7. Look over the list you just made. Take the “luckiest” number that you have tried so far (that is, the number with the highest recorded frequency so far) and enter that in the Your Choice section of the spreadsheet. Now run 10 more simulations, keeping the Your Choice selection constant. This time record the results of the numbers 123 and 333 along with your choice.
123 333 Your Choice ______
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8. Compute the totals of the three columns above.
TOTAL 123 333 Your Choice ______
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To compute the percentage of each of these totals, divide each total by 15,000 (the total number of trials now = 10 x 1500 = 15,000). Round your answers to 4 decimal places.
PERCENTAGES
123 333 Your Choice ______
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9. Lastly, compute the total and percentage for the frequency column generated in question #6 on this worksheet.
TOTAL Your 10 “Lucky Numbers”
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PERCENTAGE Your 10 “Lucky Numbers” (Again, the total divided by 15,000)
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Use the percentages you found in questions #8 and #9 to justify your answers to the following questions.
10. What’s the best strategy for choosing numbers in the “Lucky Number” spinner game?
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11. Compare the frequency of numbers with patterns, like 123 and 333, with the frequency of numbers without patterns, like 924 or 651. Which kind of number is more likely?
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12. All four percentages in questions #8 and #9 are very similar. Make a hypothesis about how you would calculate the probability of a given 3-digit number occurring on any one trial of the spinner game. That is, guess a number and decide exactly how likely that number is to occur. Explain your reasoning. (HINT: Think about fractions.)
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