Question 4 - (5+5=10 marks) [For probabilities keep 4 decimal places]
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. Since a blue ball is bigger than a red ball, we should assume the chance of randomly drawing a blue ball from any box is twice that of a red ball. From each box that you randomly choose, you draw only one ball randomly, without looking into the box or at the drawn ball. Right after a ball is drawn, its corresponding box is moved away from the table to avoid choosing the same box again. You continue this process until 25 boxes are chosen.
a) What is the probability of drawing 17 red balls and 8 blue balls from boxes with even numbered labels? (5 marks)
b) If accidentally you see the fifth ball after being drawn is red, what would be the probability of drawing 17 red balls and 8 blue balls, everything else being the same as mentioned above in the statement of problem. (5 marks)
