A biased coin has probability 0.6 of turning up heads. You win $x$ dollars if a head comes up and you lose $y$ dollars if a tail comes up. If your expected winnings is $0$ dollars, what is the relationship between x and y?
So far I have:
$P(x) = 0.6$
$P(y) = 0.4$
$E[x] = $expected winnings$ = 0$
$E[x] = x(0.6) + y(0.4) = 0$
$x = -y(0.4)/(0.6)$
I'm kind of stumped on how to continue from here, how can I use the information given to express the relationship between x and y?