## Math Forum - Problem of the Week

### Cereal Boxes and Spinners

 A cereal company has a new advertising campaign. Inside 1/6 of all cereal boxes is a \$2.00 cash prize. Inside 1/3 of all boxes is a small toy. No box contains two prizes.
Questions
1. What is the probability of opening a box and receiving no prize?

2. If you purchased 10 boxes, how many boxes should contain something (cash or toy)?

Approximately how many should contain cash? Why?

Approximately how many should contain a toy? Why?

3. Use this link to open the Spinner Java applet in a new window: NLVM Spinner.

Use the CHANGE SPINNER button. Make a spinner that BEST represents the set of probabilities.

Note: View this graphic if you need help setting up the spinner. Check with your teacher to be sure you chose the correct spinner!

4. Spin the spinner 10 times. Record your results: number of times cash is won, number of times a toy is won. Does your answer agree with your answer to question b? Must it?

5. If a box of cereal costs \$4.00 and the cash prize is \$2.00, how much did you spend to purchase the 10 boxes of cereal? How much did you earn? How many toys did you find?

6. Repeat steps (d) and (e) 9 more times. Following the 100 spins, determine: What was the total amount of money earned? How many toys did you find? If each toy is worth \$0.50, what cash value of toys did you earn?

Note: View this graphic for an illustration of how to do multiple spins.

7. Before this new advertising campaign: It cost the company \$1.50 for each box of cereal that it made and they usually sold each box for \$3.50.
What was their profit for 100 boxes?

8. During this new advertising campaign: It costs the company \$1.50 for each box of cereal that it makes, and they now sell the cereal for \$4.00.
What is their profit for 100 boxes -- taking into consideration the total value of the cash prizes and toys in these 100 boxes (use your totals from part (f))?

9. Based on your answers for (g) and (h), will this new campaign boost profits for the cereal company if the number of customers who purchase this cereal does not change? Why or why not?

10. Why might your answer be different from the person next to you?

 A cereal company has a new advertising campaign. Inside 1/6 of all cereal boxes is a \$2.00 cash prize. Inside 1/3 of all boxes is a small toy worth \$0.50. No box contains two prizes.
Questions
1. During this new advertising campaign, it costs the company \$1.50 for each box of cereal that it makes, and they sell the cereal for \$4.00.
What is their expected profit for 120 boxes -- taking into consideration the total value of the cash prizes and toys in these 120 boxes?

2. Now use the tool below to simulate actually selling 120 randomly selected boxes of cereal. You can change the spinner to BEST represents the set of probabilities by using the CHANGE SPINNER button.

Tool:NLVM Spinner.

View this graphic if you need help setting up the spinner.

View this graphic for an illustration of how to do multiple spins.

3. What is the actual profit from selling those 120 boxes of cereal?

4. Was the expected profit the same as the actual profit? Why? Do you think you would get the same expected profit if you ran the simulation again?

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