Interpreting the Expected Value of a Lottery
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:
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?
There is no error; the average loss is indeed because the vast majority of tickets lose.
The error is in assuming that the ticket buyer is penalized twice by the ticket price and the prize cost.
The error lies in using incorrect probabilities for the outcomes.
The mistake is in misinterpreting the net payoff; the winner’s actual net gain is , which when properly weighted results in an expected loss of about , not .
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