document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #255958 by jrfrunner(365) $\"\"$ $\"About$

You can put this solution on YOUR website!
understand that expected profit refers to the average profit.
\n" ); document.write( "==
\n" ); document.write( "how do you find an average?
\n" ); document.write( "well if you wanted to average the numbers 2,5,5,5,8,8,10
\n" ); document.write( "the typical person says \" add the values and divide by the numer of values\"
\n" ); document.write( "--
\n" ); document.write( "Average=(2+5+5+5+8+8+10)/7=45/7=6.43
\n" ); document.write( "but this is the same as
\n" ); document.write( "average=(2+3*5+2*8+10)/7
\n" ); document.write( " = 2/7+3*5/7+2*8/7+10/7
\n" ); document.write( " =2(1/7)+5(3/7)+8(2/7)+10(1/7)
\n" ); document.write( "or as you can see average=sum(x*P(x)), the sum of the product of the unique values times their probabilities.
\n" ); document.write( "==
\n" ); document.write( "in your problem the values are 37000 and -18000 and the respective probabilities are 0.7 and 0.3
\n" ); document.write( "--
\n" ); document.write( "so the expected profit or average profit= sum (x*P(x))=37000*(0.7)+(-18000)*(0.3)=20500
\n" ); document.write( " \n" ); document.write( "

\n" );