Find the expected payoff for a $1 bet on the box.

Question

The Tri-State Pick 3 lottery game offers a choice o several bets. You choose a three-digit number. The lottery commission announces the winning three-digit number, chosen at random, at the end of each day. The "box" pays $83.33 if the number you choose has the same digits as the winning number, in any order. Find the expected payoff for a $1 bet on the box. (Assume that you chose a number having three different digits.)

Answer 1

Ten digits exist from which you, and the lottery, can pick, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

 

The pick is a combination - the order of the numbers does not matter.

 

₁₀C₃ = 120.

 

The probability of picking the same three numbers as the lottery is 1/120.

 

The expected payoff is $1(1/120) or $0.00834.