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 $\displaystyle O \le x \le 7, 0 \le y \le 7, 0 \le x+y \le 7.$ The p.m.f. would be

combinations(X of 7)$\displaystyle *$combinations(Y of 7-X)$\displaystyle *(0.78)^{x}*0.01^{y}*0.21^{(7-x-y)}$

I can't figure out what values to use for x and y.

The support I put for B. is $\displaystyle 0 \le x \le 7

$ with p.m.f.=comb(X of 7)$\displaystyle *(0.78)^{x}*(0.22)^{(7-x)}$

I've been working on this problem, but I'm still really confused about how to perform the equations. Thank you for your help.