conditional probablity to nullify the result If two player playing a game with each other where one flip a coin and if it comes up heads he gives another X dollars and if it comes up tails she gives you Y dollars. The probability that the coin is heads is p (some number between 0 and 1.) What has to be true about X and Y to make so that both of your expected total earnings is 0. I really dont understand the question. Any explanations? **Update** E(W) = E(user1) + E(user2) 0 = -a (1-(-a)) + a (1-a) 0 = -a -a^2 + a - a^2 0 = a^2 a = 0 but options are : X=Y p/(1−p)=X/Y p/(1−p)=Y/X p=X/Y

**Outline:** I prefer to use $a$ dollars and $b$ dollars. Let random variable $W$ be the tosser's income from a toss. Then $W=-a$ with probability $p$, and $W=b$ with probability $1-p$.

Calculate $E(W)$, set it equal to $0$, and come to a conclusion about the relationship between $a$ and $b$.