Suppose that in a casino game the payout is a random variable $X$. If $X$ is positive, you gain money, if negative, you lose. Let $p(i) = P(X = i)$ and suppose that $$p(0) = \frac1{2};\quad p(1) = p(-1) = \frac{39}{220};\quad p(2) = p(-2) = \frac{3}{44}; \mbox{ and } p(3) = p(-3) = \frac{1}{220}.$$ Given that a player playing the game wins a positive amount, compute the conditional probability that...
... $X = 1$:
... $X = 2$:
... $X = 3$: