Originally Posted by

**ChrisBickle** 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 *Y*1 be the number of married executives and *Y*2 be the number of never-married executives among the three selected for promotion. The joint probability distribution of *Y*1 and *Y*2 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.