Boxes with Yellow and Green Balls

Three boxes contain yellow and green balls

  • Box 1 contains 2 yellow balls.
  • Box 2 contains 2 green balls.
  • Box 3 contains 1 yellow ball and 1 green ball.

One box is selected at random, and one ball is pulled out of that box.

  1.  The ball that is pulled out of the chosen box is yellow. What is the probability that the other ball in that same box is also yellow?
  2. Let \(A\) be the event that Box 3 is chosen. Let \(B\) be the event that a yellow ball is pulled out of the chosen box. Are \(A\) and \(B\) independent?
  3.  The ball that is pulled out of the chosen box is yellow. Without replacement, a second ball is chosen at random from one of the three boxes. (Each box has a 1/3 chance of being selected.) What is the probability that the second ball chosen is also yellow?

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