We Got A Problem #4: Chips!

Three problems about chips in a bag…

  1. A bag contains four green chips and three white chips.  You win if you can pull all the green chips before pulling all the chips of a different color.  Find the probability of winning the game.
  2. Now two red chips are added to the bag.  The rules are the same.  What is the probability of winning this game?
  3. On “The Price Is Right”, the “3 Strikes” game is played with five white chips and one red chip.  White chips are not replaced, but the red chip is.  What is the probability of pulling all five white chips before pulling the red chip for the third time?  (In the real game, after pulling a white chip the player must make a decision that might return the white chip back to the bag, so the probability of winning the full game is significantly lower.)

We’d love for readers to be able to explore these problems, so resist the urge to provide answers in the comments. Instead, we’d love helpful suggestions and ideas about different ways to think about them, successful or not. If you’d like to provide a full solution, do so with a pingback to your own blog!


About Bowen Kerins
Bowen is a mathematics curriculum writer. He is a lead author of CME Project, a high school curriculum focused on mathematical habits of mind, and part of the author team of the Illustrative Mathematics curriculum series. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won $1,000 for knowing the number of degrees in a right angle.

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