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A friend offers you the following deal: for a $10 fee you can pick an envelope from a box
containing 100 identical envelopes. However, each envelope has a different prize inside.
Ten of the envelopes contain a check for $6, eighty contain a check for 8$, six contain a check for $12,
and four contain a check for 40$.
What is your expected loss or gain if you take your friend up on their deal?
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The expected prize amount is
= 9.32 dollars.
Subtract from it 10 dollars, what you pay for the deal.
You will see that you lose 10-9.32 = 0.68 dollars = 68 cents at each deal, in average, if you do/repeat it many times.
Solved and explained.