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
