Statistics: Decision Analysis

[plewis]

A cereal manufacturer mails out 5,000,000 questionnaires to potential customers with the chance that by responding to the questionnaire, there is a
chance of winning $3,000,000. Is it worth the $0.42 postage to each
customer, if, indeed, everyone responds? Justify your answer.

[factor-fiction]

Suppose you get all 5 million questionnaires. It would cost you $5,000,000 x $0.42 = $2.1 million to post them all separately. In return you'd win $3,000,000 dollars. Sounds a good deal.
Now think of it in terms of expected return per questionnaire. The chance of yours being picked is 1 in 5 million. The expected return based on a $3,000,000 prize (assuming each questionnaire has an equal chance of winning and all take part) is $0.60 dollars ( 3 million return x one in 5 million chance). The expected return of $0.60 is greater than the cost $0.42 of the postage. So it is worth it.

[dzug]

Well no - to me the expected return is minus 42c. There's a one in 5 million chance of this NOT happening.

For me the chance is too small to be worth the bother of replying even if the payout is massive. Even if the company paid the postage (ie no layout) I doubt if I'd reply.