Raffle. There is a prize drawing for a new computer and a new stereo system. Suppose there are 1500 raffle tickets sold. The computer is worth $1000 and the stereo is worth $500. If the ticket cost $5, what is the expected value if you purchase one ticket?
To find the expected value, you need to calculate the probability of winning each prize and the respective value of each prize.
Step 1: Calculate the probability of winning the computer.
The total number of raffle tickets sold is 1500. Since there is only one computer prize, the probability of winning the computer is: 1 / 1500.
Step 2: Calculate the probability of winning the stereo system.
Similarly, the probability of winning the stereo system is also: 1 / 1500.
Step 3: Determine the value of each prize.
The computer is worth $1000 and the stereo system is worth $500.
Step 4: Calculate the expected value.
The expected value can be calculated by multiplying the probability of winning each prize by the respective value of each prize and adding the results.
Expected value = (Probability of winning computer * Value of computer) + (Probability of winning stereo system * Value of stereo system)
Expected value = (1/1500 * $1000) + (1/1500 * $500)
Now, perform the calculations:
Expected value = $0.67 + $0.33
Expected value = $1
Therefore, the expected value of purchasing one raffle ticket is $1. This means, on average, you can expect to gain $1 if you purchase a ticket.
To calculate the expected value, we need to find the probability of winning each prize and multiply it by the value of the prize.
Step 1: Calculate the probability of winning each prize.
Since there are 1500 raffle tickets sold, and you have purchased one ticket, the probability of winning the computer or the stereo is 1 out of 1500 or 1/1500.
Step 2: Calculate the expected value for each prize.
The expected value for the computer is calculated by multiplying the probability of winning (1/1500) by the value of the computer ($1000): (1/1500) * $1000 = $0.67.
Similarly, the expected value for the stereo is calculated by multiplying the probability of winning (1/1500) by the value of the stereo ($500): (1/1500) * $500 = $0.33.
Step 3: Add up the expected values.
To find the total expected value, we add the expected values of the computer and the stereo: $0.67 + $0.33 = $1.
Therefore, if you purchase one raffle ticket, the expected value is $1. This means that on average, you can expect to win $1.