1700 lottery tickets are sold for $25 each, and one grand prize of $4100 is…
2026
1700 lottery tickets are sold for $25 each, and one grand prize of $4100 is awareded. If you purchase one ticket, find your expectation per ticket .
- A.
24.99 $
- B.
- 22.59 $
- C.
2.41 $
- D.
22.57 $
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Correct answer: B
Answer: The expected value per ticket is approximately -$22.59.
Step 1: Compute the probability of winning the grand prize: 1 out of 1700, so probability = 1/1700.
Step 2: Compute the expected prize amount: (1/1700) × $4100 = 4100/1700 = 41/17 ≈ $2.4117647059.
Step 3: Subtract the ticket cost to get the net expectation: 41/17 − 25 = (41 − 425)/17 = −384/17 ≈ −22.588235294.
Step 4: Round to two decimal places: −22.588... ≈ −$22.59. The negative sign means an expected loss of about $22.59 per ticket.