SOLUTION: A contractor is considering a sale that promises a profit of $37,000 with a probability of 0.7 or a loss of (due to bad weather and such) of $18,000 with a probability of 0.3. What

Question 358536: A contractor is considering a sale that promises a profit of $37,000 with a probability of 0.7 or a loss of (due to bad weather and such) of $18,000 with a probability of 0.3. What is the expected profit?
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
understand that expected profit refers to the average profit.
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how do you find an average?
well if you wanted to average the numbers 2,5,5,5,8,8,10
the typical person says " add the values and divide by the numer of values"
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Average=(2+5+5+5+8+8+10)/7=45/7=6.43
but this is the same as
average=(2+3*5+2*8+10)/7
= 2/7+3*5/7+2*8/7+10/7
=2(1/7)+5(3/7)+8(2/7)+10(1/7)
or as you can see average=sum(x*P(x)), the sum of the product of the unique values times their probabilities.
==
in your problem the values are 37000 and -18000 and the respective probabilities are 0.7 and 0.3
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so the expected profit or average profit= sum (x*P(x))=37000*(0.7)+(-18000)*(0.3)=20500

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