Assume we have four bags A, B, C, D with 1 red and 4 green balls in bag A, 2 red and 3 green balls in bag B, 3 red and 2 green balls in bag C, and 4 red and 1 green balls in bag D. One bag is randomly selected from these 4 bags and then 2 balls are randomly drawn from the selected bag. These are one red and one green balls. Let X be the random variable which gives the number of the remaining green balls in the selected bag. Find the probability mass function (pmf) of X, the mean E(X) and variance Var(X).

Hint: Use the Bayes' theorem.