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Interpreting the Expected Value of a Lottery

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In a lottery, 10,000 tickets are sold at $1 each, with a single prize of $7,500. A researcher calculated the expected value for purchasing one ticket as follows:
E(X)=110000×(7500−1)+999910000×(−1)≈−0.25E(X)=\frac{1}{10000}\times(7500-1)+\frac{9999}{10000}\times(-1)\approx -0.25
The researcher then concluded that the average loss for a ticket holder is $1. Which of the following statements identifies the error in this conclusion?

A

There is no error; the average loss is indeed $1\$1 because the vast majority of tickets lose.

B

The error is in assuming that the ticket buyer is penalized twice by the ticket price and the prize cost.

C

The error lies in using incorrect probabilities for the outcomes.

D

The mistake is in misinterpreting the net payoff; the winner’s actual net gain is 7500−1=74997500 - 1 = 7499, which when properly weighted results in an expected loss of about $0.25\$0.25, not $1\$1.

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