1. The Cereal Box Problem By Narineh Movsessian

2. Random or Chance Outcomes SHow much precipitation is expected next year in the Kansas wheat belt? SHow many people in your town are expected to get the flu this winter? SHow much of an increase is expected in the value of a particular stock in the next two weeks?

3. “Predicting” the Future l Suppose each cereal box has one of 6 different colored pens. Orange Yellow Blue Pink Red Green l Assume chances of getting any of the 6 colored pens are equal. l How many boxes of cereal would you expect to have to buy to get a complete set of all six colored pens?

4. Method One S Conduct an experiment. S Go on a shopping trip and repeatedly buy cereal boxes until you get a pen of each color. S This ends one shopping trip. S Repeat this process.

5. Results of One Shopping Trip Shopping Trip OrangeYellowPinkRedGreen # of Boxes 1//// Blue /////////////////21 We see that we bought 21 boxes of cereal before we had a complete set.

6. Method Two S Use a six sided die as a physical model for buying cereal boxes. S Randomly let 1=orange 2=yellow 3=blue 4=pink 5=red 6=green S One toss of the die will correspond to the purchase of one box.

7. Results of Shopping Trips Shopping Trip OrangeYellowBluePinkRedGreen # of Boxes 1/////////////////////21 2///// ////////16 3 4 5 / // //////////// // //// ///// //// /// / // / / /// / /////// 14 13 28

8. l Our experiment gives us an average of The Statistic of Interest l So on average one would have to buy about 19 boxes of cereal in order to get all 6 colors of pens.

9. Method Three S Using computer generated random numbers to simulate the experiment. S The actual expected value was found using method three over a large number of trials, about 10,000. S The actual average is 14.7.

10. Can use graphs to organize the data. Histogram #1Histogram #2 Graphs