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.

- 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?
- 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?
- 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?