Geometric Distribution problem


I have a quick question:

1. I have a universe that has 40% of it with a condition Z (Success).
2. Of those 40%, 15% of them have condition A.
3. Also of those 40% with condition Z there are 5% with condition B.

Question: What % of the population will meet condition A within 8 tries OR condition B within 20 tries?

I was thinking:
2. should be NBD(7,1,.15)
3. should be NBD(19,1,.05)

then add those two probs together, right?