Math Forum - Problem of the Week


Dice Sums

If you roll a pair of dice 100 times, and each time add the two outcomes, what will be the sum that appears the most often? For example, about how many times do you think the sum will be 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12?
  1. Make a prediction.
  2. Test to see if your hypothesis was correct. Use the following site http://www.shodor.org/interactivate/activities/ExpProbability/ to help you gather the information.
  3. Try the experiment five times to see if you notice any patterns. Which sums appear most often? Here is a sample spreadsheet [dice_sums.xls] that you may use after listing all the possible outcomes. What pattern do you notice when listing the favorable outcomes?
  4. What do you notice about the results each time you tried the experiment?
  5. Was your prediction correct?

For further exploration: If you used three dice instead of two, what do you think would be the sums that would occur most frequently? Give evidence to support your conclusion. (You may want to make a list of all possible outcomes.)


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