Hey I'm new here, but I would like to hear the answer to this one.

I'm sure I'm doing this wrong. Could someone correct me?

All bowls have a 1/5 chance of being selected. In order to select two white balls bowl 2, 3, 4 or 5 must be selected (since bowl 1 only has 1 white ball).

So the chances of getting 2 white balls should be:

1/5 * (the chance of picking 2 white balls from bowl 2) + 1/5 * (the chance of picking 2 white balls from bowl 3 + .... + 1/5 * (the chance of picking 2 white balls from bowl 5)

If bowl 2 is selected there is a 2/5 chance of getting a white ball and then a 1/4 chance of getting another one. So the chance of selecting bowl 2, and getting two white balls out of it is 1/5 * (2/5 * 1/4) = 1/50. Applying this same logic to the other bowls gives me:

So there is a 40% chance of selecting 2 white balls, right?

So to answer B) I think it would be that if we selected 2 white balls, we must have selected either bowl 2, 3, 4 or 5. Now we only have 4 possible bowls that were selected. So I believe our equation would end up being

Therefore, we end up with:

So that should be a 15% chance of having gotten the 2 white balls from bowl 3. Right?

Is that at all correct?