Question 1192577
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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


    {{{(6*10 + 80*8+ 6*12 + 4*40)/100}}} = 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.
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Solved and explained.