marginal probability distribution and finding a probability
Im kinda lost on this problem once i figure out the distribution it shouldnt be hard to figure out the probability or independence.
1. Of nine executives in a certain business firm, four are married, three have never married, and two are divorced. Three executives are selected for promotion. Let Y1 be the number of married executives and Y2 be the number of never-married executives among the three selected for promotion. The joint probability distribution of Y1 and Y2 is
f(x,y) = (4chooseX)x(3chooseY)x(2choose3-X-Y)/(9choose3)
where x and y are integers such that 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, and 1 ≤ x + y ≤ 3.
a. Find the marginal probability distribution of X.
b. Find P(X | Y = 2).
c. Are X and Y independent? Explain your answer.