In the lottery called Pick 4, a person pays $1 and then picks a four numbers. Then four numbers are randomly generated, each from 0 to 9, equally likely and independently.
If all the four randomly generated match the four numbers that the person picks, the person wins $9000
(For instance, if the person picks 1225 and the winning numbers are 1522, 1252, 2512 etc, the person wins)
A) At the best, how much is the player's expected earning? Is it above or below $1?
B) To make the lottery a fair bet, how much should the winning bonus be ? (i.e. find X, such that if the winning bonus is $X. the player's expected earning equals $1)