Q: There are 5 black balls and 3 white balls in a bag. Three balls are chosen at random from the bag without replacement. Given that of the three balls chosen, at least one black ball and at least one white ball was chosen, what is the probability that two black balls were chosen?

My answer: 2/3. Can anybody try to disprove this? Other possible answers: 11/56, 45/56, 4/9, 1/2 (multiple choice question).