To calculate the expected winnings for a person who buys one raffle ticket, we first need to determine the total number of raffle tickets sold and the prizes available.
- Total tickets sold: 2000 tickets
- Ticket price: $3
Prizes and their values:
- First prize (flat-screen TV): $500
- Second prize (android tablet): $375
- Third prize (e-reader): $200
- Five $25 gift certificates: \(5 \times 25 = 125\)
Total prize value:
- Total prize money = \(500 + 375 + 200 + 125 = 1200\)
Probabilities of winning each prize:
- Probability of winning the first prize: \( \frac{1}{2000} \)
- Probability of winning the second prize: \( \frac{1}{2000} \)
- Probability of winning the third prize: \( \frac{1}{2000} \)
- Probability of winning a $25 gift certificate: \( \frac{5}{2000} = \frac{1}{400} \)
Expected value from each prize:
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Expected value from the first prize: \[ \frac{1}{2000} \times 500 = 0.25 \]
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Expected value from the second prize: \[ \frac{1}{2000} \times 375 = 0.1875 \]
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Expected value from the third prize: \[ \frac{1}{2000} \times 200 = 0.1 \]
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Expected value from one gift certificate: \[ \frac{1}{400} \times 25 = 0.0625 \] Since there are 5 gift certificates, we multiply this by 5: \[ 5 \times 0.0625 = 0.3125 \]
Total expected winnings:
Now, we add the expected values for all prizes together: \[ 0.25 + 0.1875 + 0.1 + 0.3125 = 0.85 \]
Final calculation for expected winnings:
The total expected winnings from one ticket is $0.85.
Conclusion:
Therefore, the expected winnings for a person who buys one raffle ticket are $0.85.
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