BUS 510.601 In the lottery called Pick 4, a person pays $1

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)

 

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