Question

Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont. You choose a three-digit number; the state chooses a three-digit winning number at random and pays you $500 if your number is chosen. Because there are 1000 three-digit numbers, you have probability 1/1000 of winning. Taking X to be the amount your ticket pays you, the probability distribution of X is Payoff X Probability: $0.00 0.999 What is your average payoff from many tickets

Answer 1

For many(n) tickets, the average payoff is 0.5n, in which n is the number of tickets.

Explanation:

1/1000 chance of winning.

This means that there is an 1/1000 probability of you earning $500.

1 - 1/1000 = 999/1000 chance of losing.

In this case, you earn nothing.

What is your average payoff from many tickets

`A = (500*1)/(1000) + (0*999)/(1000) = (500)/(1000) = 0.5`

Your average payoff from a ticket is 0.5. So for many(n) tickets, the average payoff is 0.5n, in which n is the number of tickets.