A lottery ticket which pays $1 million dollars will only cost you $1 dollar. To win a person must match 5 numbers from a total of 59 numbers. What is the expected payoff if you purchase one ticket?

A) $0.20

B) $0.80

C) - $0.20

D) - $0.80

First we have to calculate the probability that a person wins a lottery with just one ticket:

The number of the combinations:

59 C 5 = (59 * 58 * 57 * 56 * 55) / (5 * 4 * 3 * 2 * 1) = 5,006,386

So the probability to win is:

1 : 5,006,386 = 0.0000002

$1,000,000 - 0.0000002 = $0.2 (gain)

and if a ticket costs $1:

$1 - $0.2 = $0.8 (loss)

Answer: D) - $0.8