An urn has 1 red ball, 2 blue balls, and 1 green ball. A ball will be selected

at random. If it is not red, you stop. If it is red, it is put back in the urn

and a ball is again selected at random, and then you stop. So in total, you

select one or two balls. Let X be the number of red balls you selected, and

let Y be the total number of blue balls selected.

1. Give the conditional probability mass function of Y, given X = 0.
2. Are X and Y independent? Please justify your answer mathematically.