In Ohio’s Pick 4 game, you pay $1 to select a sequence of four digits, such as 7709. If you buy only one ticket and win, your prize is $5000 and your net gain is $4999.
a. If you buy one ticket, what is the probability of winning?
b. Construct a table describing the probability distribution corresponding to the purchase of one Pick 4 ticket.
c. If you play this game once every day, find the mean number of wins in years with exactly 365 days.
d. If you play this game once every day, find the probability of winning exactly once in 365 days.
e. Find the expected value for the purchase of one ticket.