APFIVE 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:
$$E(X)=\frac{1}{10000}\times(7500-1)+\frac{9999}{10000}\times(-1)\approx -0.25$$
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?
The error lies in using incorrect probabilities for the outcomes.
There is no error; the average loss is indeed $$\$1$$ because the vast majority of tickets lose.
The mistake is in misinterpreting the net payoff; the winner’s actual net gain is $$7500 - 1 = 7499$$, which when properly weighted results in an expected loss of about $$\$0.25$$, not $$\$1$$.
The error is in assuming that the ticket buyer is penalized twice by the ticket price and the prize cost.
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