1. ## pmf and support

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 $O \le x \le 7, 0 \le y \le 7, 0 \le x+y \le 7.$ The p.m.f. would be
combinations(X of 7) $*$combinations(Y of 7-X) $*(0.78)^{x}*0.01^{y}*0.21^{(7-x-y)}$

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

The support I put for B. is $0 \le x \le 7
$
with p.m.f.=comb(X of 7) $*(0.78)^{x}*(0.22)^{(7-x)}$

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

2. Originally Posted by logitech
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. [snip]
What about the other 50% ....?

3. I'm sorry. The 28% was supposed to be 78% prefer to date nonsmokers. I'm not sure how the combination parts should be written to show the proper formula. Any help would be great!