Alottery 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 )
D ) - $0.8