Say your roommate says that she has a dog and will make you 10:1 odds if you can guess her dog's weight to within +/- a set amount. What set amount would you ask her for to make the game fair (expected value 0)?
My work
p/(1-p) = 10
p = 10(1-p)
p = 10 - 10p
11p = 10
p= 10/11
let the amount be x
E(X) = x *p + (1-p)(-x)
= x*10/11 + 1/11 (-x)
= 9x/11
hence x = 0 what is wrong here ? what is correct solution ?