200 tickets are sold to a raffle. It costs $5 to buy a ticket. There is one first prize winner and one second prize winner. First prize is $500. Second prize is $250. What is the value of playing this game?
To calculate the value of playing this game, we need to find the expected value. The expected value is the sum of the products of each possible outcome and its respective probability.
First, let's calculate the total cost to buy all the tickets:
Total cost = Number of tickets * Cost per ticket
Total cost = 200 tickets * $5
Total cost = $1000
Next, let's calculate the probabilities of winning each prize:
Probability of winning first prize = 1 / Total number of tickets
Probability of winning first prize = 1 / 200
Probability of winning first prize = 0.005
Probability of winning second prize = 1 / Total number of tickets
Probability of winning second prize = 1 / 200
Probability of winning second prize = 0.005
Now, let's calculate the expected value for each prize:
Expected value of first prize = Probability of winning first prize * Value of first prize
Expected value of first prize = 0.005 * $500
Expected value of first prize = $2.50
Expected value of second prize = Probability of winning second prize * Value of second prize
Expected value of second prize = 0.005 * $250
Expected value of second prize = $1.25
Finally, let's calculate the overall expected value:
Overall expected value = Expected value of first prize + Expected value of second prize
Overall expected value = $2.50 + $1.25
Overall expected value = $3.75
Therefore, the value of playing this game is $3.75.
To find the value of playing this game, we need to calculate the expected value. The expected value is the sum of each possible outcome multiplied by its respective probability.
First, let's calculate the total cost of buying all the tickets. Since there are 200 tickets sold, and each ticket costs $5, the total cost is 200 * $5 = $1000.
Now, we can calculate the probability of winning each prize. There is only one first prize winner out of 200 tickets, so the probability of winning the first prize is 1/200. Similarly, there is only one second prize winner out of 200 tickets, so the probability of winning the second prize is also 1/200.
Next, let's calculate the value of each prize. The first prize is $500, and the second prize is $250.
Now we can calculate the expected value of playing this game:
Expected Value = (Probability of winning first prize * Value of first prize) + (Probability of winning second prize * Value of second prize)
Expected Value = (1/200 * $500) + (1/200 * $250)
Expected Value = $2.50 + $1.25
Expected Value = $3.75
Therefore, the expected value of playing this game is $3.75.