Questions: Angelo's Pizza is having a ticket raffle to raise money for new soccer uniforms. A 1 ticket gives an even chance to win one 25 gift certificate, one 15 gift certificate, or three 5 gift certificates. What is the expected profit or loss for purchasing 1 ticket if 100 total tickets are sold? a loss of 0.55 a loss of 0.45 a gain of 0.55 a gain of 0.45

Solution Steps

The possible outcomes for purchasing one ticket are:

• Winning a \$25 gift certificate.
• Winning a \$15 gift certificate.
• Winning one of the three \$5 gift certificates.
• Not winning anything.

Since there are 100 tickets sold, the probabilities are:

• Probability of winning \$25: \( \frac{1}{100} \).
• Probability of winning \$15: \( \frac{1}{100} \).
• Probability of winning \$5: \( \frac{3}{100} \).
• Probability of not winning anything: \( \frac{95}{100} \).

The expected value \( E \) is calculated as: \[ E = \left(\frac{1}{100} \times 25\right) + \left(\frac{1}{100} \times 15\right) + \left(\frac{3}{100} \times 5\right) + \left(\frac{95}{100} \times 0\right) \] \[ E = 0.25 + 0.15 + 0.15 + 0 = 0.55 \]

The cost of purchasing one ticket is \$1. The expected profit or loss is: \[ \text{Expected Profit or Loss} = \text{Expected Value of Winnings} - \text{Cost of Ticket} \] \[ \text{Expected Profit or Loss} = 0.55 - 1 = -0.45 \]

This means there is an expected loss of \$0.45.

Final Answer