One thousand tickets ae sold at $1 each for a grand prize of $500.00. What is the expected value if a person purchases a single ticket?
Part 2:are the people selling the tickets making a profit? Why or why not.
To calculate the expected value, we need to determine the probability of winning and the associated payoff.
Let's break down the problem:
1. Probability of winning:
The probability of winning depends on the number of tickets sold and the total tickets purchased. In this case, there are 1000 tickets and a person is purchasing a single ticket. Therefore, the probability of winning is 1/1000, or 0.001.
2. Payoff:
The payoff is the amount of money received if you win. In this case, the grand prize is $500.
Now, we can calculate the expected value (EV):
EV = (Probability of winning) * (Payoff) + (Probability of not winning) * (Payoff if not winning)
EV = (0.001 * $500) + (0.999 * $0)
EV = $0.50
So, the expected value of purchasing a single ticket is $0.50. This means that on average, a person buying one ticket can expect to receive $0.50.
Part 2: Are the people selling the tickets making a profit?
The people selling the tickets are making a profit because the expected value of purchasing a single ticket is $0.50, while the price of a ticket is $1. This means that for every ticket sold, they are making a profit of $0.50 per ticket sold. Since they sold 1000 tickets, their total profit would be $0.50 * 1000 = $500.