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Probability

August 1, 2008

We played “Pig,” a simple probability game that has become a regular for us. This game provides practice with addition up to sums of 24 along with intuitive experience with probability.

  1. In turn, each player is handed four dice. He can choose to roll 1, 2, 3 or all 4 dice. He can roll as many times as he likes.
  2. Each time he rolls, he computes the sum of all the dice he rolled. That is his score.
  3. If he rolls one “1” at any point, his turn ends, and he loses all the points he’s scored in that round.
  4. If he rolls two “1”s — his turn ends, and he loses all the points he’s scored so far in the whole game.
  5. The first player to reach 100 points wins.

Since I’m focusing a bit on adding without counting, I modeled logical ways of adding the numbers on the dice. For example, if you roll 5, 6, 5 & 4 … group the 6 & 4 together and the 2 5’s together. Two 10s is 20.

We had a round when Sarah and I both chose to roll only two dice and rolled two “1”s. (VERY bad luck!) After the game, I asked Sarah and James what they thought were the odds of that happening. Since the chances of rolling a “1” when you roll one die is 1:6, they thought the odds of rolling 2 “1”s when 2 dice are rolled would be 2:12. I pointed out that 2:12 is the same as 1:6. Since James hasn’t studied fractions yet, I drew a diagram to show him why this was so. Then I asked, “So you think the chances of rolling a “1” with one die are the same as the odds of rolling two “1”s when you roll 2 dice? They confirmed that this was their prediction. Even though we’ve done the tree diagram thing before, it hasn’t sunk in yet. 😉

So I showed them, using a simple tree diagram, why the odds of rolling two dice and getting two “1”s are actually much lower (1:36)

(Poking around online, I just found a link that explains this.)

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