Introduction: Often cereals have free items that can be found in the cereal box. One cereal advertised you would find "Free Inside, One Hockey Card". There were six different hockey player cards and they wanted you to "Collect All Six". In this problem we experiment with probabilities of collecting all six cards.

Problem: Suppose you buy one box at a time of this kind of cereal. You find the hockey card in the box and place it on a shelf. You continue to buy other boxes until you have collected all six different cards. Roll a die (singular of dice) to simulate this experiment. (Each roll of the die will represent buying one box of cereal and finding one type of card.)

1. Show the results of your experiment (the set of cards collected until you get at least one of each type of card).
2. Repeat the experiment of question 1 twenty times. This simulates 20 different people each trying to collect the six different cards. What assumptions are you making in your simulation?
3. Which of the following percentages do you think is the probability (chance) of collecting all six different cards if you buy only six boxes of cereal?

   A. less than 2%   B. about 10-15%    C. about 20-25%    D. about 50%

   Explain why you chose the answer you did.

4. Your friend wants to buy boxes of cereal to collect all six different cards. She wants to know about how many boxes she will need to buy (she intends to buy them all at once, not wanting to make many trips to the grocery store). How many boxes will you recommend she buys? Explain how and why you will suggest that number.
5. If the cereal company expands its hockey card promotion to a total of 12 different cards, describe how you would design a simulation to show buying cereal until you collect all 12 different cards (and so you could answer questions similar to 1-4).

Materials: die (singular of dice), pencil, paper, calculator

Probability, data management, numbers and operations, critical and creative thinking, communication

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
Include in your portfolio?
Yes     No     Optional 
Toward Your Marks?
Yes     No     Optional 

  Hints:

You may wish to use or create other materials to simulate the experiment in question 5.