Fifty boxes labeled with numbers from 1 to 50 are laid on a table. In each box there is a blue ball and a red ball. From each box that you randomly choose, you pick only one ball randomly, without looking into the box. Right after a ball is picked up, its corresponding box is moved away from the table to avoid picking the same box again. You continue this process until 25 boxes are chosen.
a) What is the probability of picking 8 blue balls and 17 red balls from boxes with even numbered labels?
b) If accidentally you see the fifth ball after being picked up to be Red, what would be the probability of picking 8 blue balls mentioned as above.
