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
1/1000 * 500
of course there's a profit. ticket sales are $1000, and the prize is only $500.
To calculate the expected value of purchasing a single ticket, we need to multiply the probability of winning by the corresponding payout, and then subtract the cost of the ticket.
Given:
- Total number of tickets sold = 1000
- Cost of a single ticket = $1
- Grand prize amount = $500
Step 1: Calculate the probability of winning
Since there is only one grand prize, the probability of winning is 1/1000.
Step 2: Calculate the expected payout if the person wins
If the person wins, they will receive $500.
Step 3: Calculate the expected value
Expected value = (Probability of winning * Payout if win) - Cost of ticket
Expected value = (1/1000 * $500) - $1
Expected value = $0.50 - $1
Expected value = -$0.50
Therefore, the expected value of purchasing a single ticket is -$0.50, which means the person can expect to lose $0.50 on average.
Part 2: Are the people selling the tickets making a profit?
Yes, the people selling the tickets are making a profit. Since the expected value of purchasing a single ticket is negative, it indicates that on average, the ticket buyers lose money. The difference between the cost of the ticket and the expected value ($1 - (-$0.50)) results in a profit for the ticket sellers of $1.50 per ticket.
To find the expected value of purchasing a single ticket, we need to calculate the probability of winning the grand prize and the amount of money that would be gained or lost in that scenario.
Part 1:
The probability of winning the grand prize can be found by dividing the number of winning outcomes by the total number of possible outcomes. In this case, there is only one winning outcome (the person wins the grand prize) and 1,000 possible outcomes (since there are 1,000 tickets sold). Therefore, the probability of winning the grand prize is 1/1,000.
The amount of money gained or lost can be calculated by subtracting the ticket price from the grand prize amount. In this case, the amount gained would be $500 - $1 = $499 if the person wins, and $0 if the person loses.
Next, we calculate the expected value by multiplying the probability of winning by the amount gained or lost in that scenario, and adding up all possible outcomes:
Expected Value = (Probability of Winning * Amount Gained) + (Probability of Losing * Amount Lost)
Expected Value = (1/1,000 * $499) + (999/1,000 * $0)
Expected Value = $0.499 + $0
Expected Value = $0.499
Therefore, the expected value of purchasing a single ticket is $0.499.
Part 2:
In this case, the people selling the tickets are making a profit. Each ticket is sold for $1, and the expected value of purchasing a single ticket is $0.499. Since the expected value is less than the ticket price, the seller is gaining more money from ticket sales than they would be expected to pay out in winnings, resulting in a profit for the seller.