Question: Finding expected value for New Jersey’s Pick 4 Game

In New Jersey’s Pick 4 lottery game, you pay 50 cents to select a sequence of four digits, such as 7273. If you win by selecting the same sequence of four digits that are drawn you collect $2788.00.

a. How many different selections are possible?

b. What is the probability of winning?

c. If you win, what is your net profit?

d. Fine the expected value.

e. An example in the section showed that if you bet 50 cents in the NJ Pick 3 game, your expected value is -22.5cents. Which is the better game: New Jersey’s Pick 3 game or Pick 4 game? Why?