Question

You can buy a lottery ticket for $500.

The odds are as follows:

1 in 10 tickets will pay $750.

1 in 100 tickets will pay $1000.

1 in 1000 tickets will pay $200,000.

1 in 10,000 tickets will pay $1,000,000.

1 in 100,000 tickets will pay $10,000,000.

a. What is the expected value of the ticket to you?

b. Should you buy the ticket? Explain your decision.

Answer 1

(a)

x	P(x)	x * P(x)
250	0.1	25
500	0.01	5
199500	0.001	199.5
999500	0.0001	99.95
9999500	0.00001	99.995
-500	0.99995	-499.975

Expected value = ∑x * P(x) = $-70.53

(b) Since the expected value < 0, you should not buy the ticket