A roulette from a casino contain 18 red cases, 18 black cases and 1 green cases. A player shows up with $10$dollars. He decides to bet $1$dollar on red 10 consecutives times. If it's red, he wins a dollar and if not he loses his dollar. Let $S$ be the the amount of money the player has after 10 bets. Find the value $S$ can have, then calculate $P(S<3|S\leq18)$.
So the value S can take is every natural numbers $0\leq S\leq20$
but after that I'm confused on how to proceed. I guess we could do it using a density function but i don't know how.
Any help to point me in the right direction would be greatly appreciated.