Question

Expected Value for the Ohio Pick 4 Lottery In the Ohio Pick 4 lottery, you can bet $1 by selecting four digits, each between 0 and 9 inclusive. If the same four numbers are drawn in the same order, you win and collect $5000?

a. How many different selections are possible?
b. What is the probability of winning?
c. If you win, what is your net profit?
d. Find the expected value for a $1 bet.

Answer 1

a) There are `10^4 = 10000` ways of picking your numbers .

b) There is only one way you can win, if the numbers have to be in the exact order you picked, so that probability is `1/10000`.

c) Assuming you win on the first ticket, your net profit will be `$5000 - $1 = $4999`, because you will have paid one dollar to buy a ticket.

d) We have:

`Ev = ["P(win)"xx("net gain")] + ["P(loss)" xx ("net loss")]`

`color(white)(Ev) = 0.0001(5000-1) + 0.9999(–1)`

`color(white)(Ev) = –$0.50`

Hopefully this helps!