Math Forum - Problem of the Week

Box Model

In math class you are learning about probability. Your assignment is to design a fair game for your classmates to play. Your game idea is for two players and uses the Box Model applet.

One player is called 24 and the other is called 30. The numbers 1 through 10 are placed in the box. You have the computer pick 20 numbers (a number is replaced after each pick). On each draw, a player scores a point if the number drawn is a factor of your name. On any draw it is possible that both players score a point, only one player scores a point, or no players score a point. Whoever has the most points after 20 draws is the winner.

Play the game with a friend at least 5 times.


  1. Do you agree that it is a fair game?
  2. What is the probability that 24 will score a point when a number is drawn?
  3. What is the probability that 30 will score a point when a number is drawn?
  4. Would the probabilities change if you replaced the number 7 with the number 12?

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