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Posted Mon Jul 21 11:47:29 PDT 2008 by Randall Hudson (Randall Hudson).

Huntsville High School, Huntsville, USA

Materials Required: Active minds

Activity Time: 45 minutes

Concepts Taught: Probability/Finite Math

Start with the question: what would be the best strategy to guess the numbers of two six sided dice rolled at the same time? Give the students some time to think. Hopefully, hope springs eternal, they will come up with the two types of guesses--either doubles, snake-eyes, etc., or two different numbers for their guess, say 3 and 4. If they don't come up with this on their own help them along. Most students, even with some probablity background, will become confused at this point (almost all probability questions that they are familiar with will have only one possible probability outcome--this problem has two). Here we should help the students further by using a simpler example: Ask them what their guessing strategy should be for two coins tossed at the same time. This most students should be able to reason out--If they choose two different outcomes, heads and tails, they will be guaranteed of guessing one of the coin tosses and so have a 1/2 chance of guessing the two coin tosses correctly; If they choose a double outcome, both heads or both tails, they will have only 1/4 chance of guessing the coin tosses correctly. Now return to the topic question and ask again: What is the best strategy to guess the outcome of two six sided dice rolled at the same time? At this point the students should be able to reason it out--if they choose two different numbers the probability of guessing one die roll correctly will be 2/6 (1/3) and the probability of guessing the other die roll will be 1/6 so the probability of guessing both dice rolls would be 1/3 times 1/6 or 1/18. If they choose doubles the probability of guessing one of the die rolls would be 1/6 as would the second, so we would have the probability of guessing both dice rolls of 1/6 times 1/6 or 1/36. Ask the students if they understand the principle involved. Of course they will say yes. Then verify this with a pop quiz of: What would be the best strategy to guess the outcome of three six sided dice rolled at the same time?