Suppose that you are offered the following "deal." An impartial person selects an integer between 1 and 9 at random and you try to guess beforehand which number will be selected. If you guess wrong then you pay $1 and if you guess right then you win $10.
Call the outcome of the game your "gain." (Note that if you pay money then your gain is negative.)
In this game your probability of winning is:
a. Larger than your probability of losing.
b. Smaller than your probability of losing.
c. Equal to your probability of losing.
d. Unknown.