This is actually a very difficult question... lets say the Prostitute will stay home and conduct her business there, but remember the the Witch will still be in the house (home) because she does not need to go out and attend her evil meetings, she can do it in her sleep whiles in the house...this put the Witch in a very good position to be the answe.
The armed robber cannot rob his own house and therefore have to go out and conduct his robbery. Prostitute mostly go out to practice prostitution with their clients... but Witches can attend her meeting or whatever without actually been there in person......
now "who will stay at home at night???" this refers to only one person, THIS MAKES YOUR ANSWER VERY WRONG