Five identical bowls are labeled 1,2,3,4 and 5. Bowl i contains i white and 5 - i black balls with i = 1, 2, 3, 4, 5. A bowl is randomly selected and two balls are randomly selected (without replacement) from the contents of the SAME bowl.
a. What is the probability that both balls selected are white?
b. Given that both balls selected are white what is the probability that bowl 3 was selected?