1. A jar contains five blue balls and five red balls. You roll a fair die once. Next you randomly draw (without replacement) as many balls from the jar as the number of points you have rolled with the die.

Question

(a) What is the probability that all of the balls drawn are blue?
(b) What is the probability that the number of points shown by the die is r given that all of the balls drawn are blue?

Answer 1

P(n) = 1/6
Clearly, P(6 blues) = 0
P(n blues) = 5*4*3*.../(1*2*...n) = 5Cn
so P(n & n blues) = 5Cn/6 for 0<n<6

Answer 2

oops. I got the denominator in the wrong order.
P(n) = 5/6 * 4/5 * ... n factors = 5*4*3.../(6*5*4...)
= 5Pn*(6-n)!/6!