# How does it possible that $ZPP=RP\cap coRP$?

How does it possible that $ZPP=RP\cap coRP$ ?
After all, it must be that $RP\cap coRP = \emptyset$
Where Am I wrong ?

• What makes you think that their intersection is empty? – rus9384 Aug 24 '17 at 22:45

## 1 Answer

The complexity class P is obviously contained in their intersection (since the probability to err on either side is zero), so the intersection isn't empty.

(The complement of a complexity class isn't the same as the complement of a specific language.)