Answer:
<u>The expected value of every ticket is a loss of $ 1.35</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Number of tickets sold at the raffle = 1,500
Price of each ticket = $ 2
Total prizes = 1 * $ 500 + 1 * $ 250 + 1 * $ 150 + 1 * $ 75
2. Use a probability distribution table to calculate the expected value of your gain. Your expected value is_____ ?
Let's answer the question using a probability distribution for the gains, this way:
- Probability of 1st prize of $ 498 (500 - ticket) = 1/1,500
- Probability of 2nd prize of $ 248 (250 - ticket) = 1/1,500
- Probability of 3rd prize of $ 148 (150 - ticket) = 1/1,500
- Probability of 4th prize of $ 73 (75 - ticket) = 1/1,500
- Probability of losing $ 2 (ticket) = 1,496/1,500
Now, we calculate the mean for all the tickets (winners and non-winners), this way:
Expected value = [(1,496 * -2) + (1 * 498) + (1 * 248) + ( 1 * 148) + ( 1 * 73)]/1,500
Expected value = [- 2,992 +498 + 248 + 148 + 73)/1,500
Expected value = -2,025/1,500 = - 1,35
<u>The expected value of every ticket is a loss of $ 1.35</u>
