In a smoking survey among boys between the ages of 12 and 17, 28% prefer to date nonsmokers, 1% prefer to date smokers and 21% don't care. Suppose 7 such boys are selected randomly and X equals the number who prefer to date nonsmokers and Y equals the number who prefers to date smokers.
A. Determine the joint p.m.f. of X and Y. Be sure to include the support of the p.m.f.
B. Find the marinal p.m.f. of X. Again include the support.
The support for A. I figured was The p.m.f. would be
combinations(X of 7) combinations(Y of 7-X)
I can't figure out what values to use for x and y.
The support I put for B. is with p.m.f.=comb(X of 7)
I've been working on this problem, but I'm still really confused about how to perform the equations. Thank you for your help.