I was wondering if I could get some help with a problem. I have thought about this for a long time and can't figure it out. I don't need to solve the problems (at least not yet), I just need to know if they have different answers and if so, why. I thought they should all have the same answer, but my calculations are not working out that way :-(

Imagine a glass with 6 white balls numbered 1-6 and 4 black balls numbered 1-4. 3 balls are chosen at random.

A) What is the probability you choose 3 white balls given you choose at least 1 white ball.

B) What is the probability you choose 3 white balls given you choose at least 1 even numbered white ball?

C) What is the probability you choose 3 white balls given you choose white ball #2?