Suppose that in a casino game the payout is a random variable if is positive, you gain money, if negative, you lose. let == and suppose that p(0)=15; p(1)=p(−1)=2275; p(2)=p(−2)=110; and p(3)=p(−3)=1150. given that a player playing the game wins a positive amount, compute the conditional probability that.
(a)- x=1 :
(b)- x=2 :
(c)- x=3 :

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.