KöMaL 2018 B4959

Barnaby has $n$ marbles in his pocket. When he performs a somersault, each marble has a probability of $0<p<1$ to fall out of his pocket, independently of one another. If at least one marble falls out during a somersault then Barnaby will stop performing somersaults. Otherwise he will continue. Given that the probability of having an even number of marbles in his pocket when he stops doing somersaults is 50%, what may be the value of $n$?