Question

Suppose your neighbors kid comes by to offer you a lottery ticket for the school fundraiser. There are 700 tickets sold and each are $10. The prizes are as follows: 1st ticket drawn = $500 2nd ticket drawn = $250 3rd ticket drawn = $100 If all 700 tickets are sold, what is your expected value if you buy a ticket?

Answer 1

Answer: $1.21

Explanation:

1. Calculate the probability of winning each prize

• For the 1st ticket drawn, there is a 1/700 chance of winning

• For the 2nd ticket, there is a 1/699 chance of winning (since 1 ticket has already been drawn)
• For the 3rd ticket, there is a 1/698 chance of winning (since 2 tickets have already been drawn)

2. Calculate the value of each prize

• The 1st ticket has a value of $500

• The 2nd ticket has a value of $250

• The 3rd ticket has a value of $100

3. Multiply the probability of winning each prize by the value of each prize

• For the 1st ticket, the expected value is (1/700) * $500 ≈ $0.71
• For the 2nd ticket, the expected value is (1/699) * $250 ≈ $0.36.
• For the 3rd ticket, the expected value is (1/698) * $100 ≈ $0.14.

4. Sum up the expected values

• Add the expected values of all the prizes together.
• $0.71 + $0.36 + $0.14 = $1.21.