Question

Valley View Elementary is trying to raise money to buy tablets for their classrooms. They sell 2000 raffle tickets at $3 each. First prize is a flat-screen TV worth $500. Second prize is an android tablet worth $375. Third prize is an e-reader worth $200. Five $25 gift certificates will also be awarded. What are the expected winnings for a person who buys one ticket?

Answer 1

To calculate the expected winnings for a person who buys one raffle ticket, we need to consider the probability of winning each prize, the value of each prize, and the total number of raffle tickets sold.

1. Total number of tickets sold: 2000

2. Prizes and their probabilities:

   • First prize (TV worth $500):

     • Probability of winning = 1/2000
     • Expected value from first prize = \( \frac{1}{2000} \times 500 = 0.25 \)

   • Second prize (Tablet worth $375):

     • Probability of winning = 1/2000
     • Expected value from second prize = \( \frac{1}{2000} \times 375 = 0.1875 \)

   • Third prize (E-reader worth $200):

     • Probability of winning = 1/2000
     • Expected value from third prize = \( \frac{1}{2000} \times 200 = 0.1 \)

   • Five $25 gift certificates:

     • Probability of winning one of the gift certificates = 5/2000
     • Expected value from gift certificates = \( \frac{5}{2000} \times 25 = \frac{125}{2000} = 0.0625 \)

3. Total expected winnings: Now we sum the expected values from each prize: \[ \text{Total Expected Winnings} = 0.25 + 0.1875 + 0.1 + 0.0625 = 0.6 \]

Thus, the expected winnings for a person who buys one raffle ticket is $0.60.