In the Arizona state lottery, a player chooses four digits, which must be in a specific order. Note that the numbers may lead with the digit 0. Digits may also be repeated. In each lottery drawing, a four-digit sequence is selected. Any player with a lottery pick matching all four digits, in the correct order, receives a payout of $1,000.

a. Determine the probability of winning this lottery game.

b. Calculate the expected value of winning if it costs $5 to play one game. Interpret the expected value.

c. Determine a fair cost for an individual to play this lottery game.