SOLUTION: 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. T

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Question 1192577: 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?
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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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


    %286%2A10+%2B+80%2A8%2B+6%2A12+%2B+4%2A40%29%2F100 = 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.