document.write( "Question 405479: . Essay; show all work. A community 5K run will award $50 to the winner. 55 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent. \n" ); document.write( "
Algebra.Com's Answer #286380 by stanbon(75887)\"\" \"About 
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A community 5K run will award $50 to the winner. 55 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.
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\n" ); document.write( "Find expected value.
\n" ); document.write( "P(win) = 1/55
\n" ); document.write( "P(lose) = 54/55
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\n" ); document.write( "\n" ); document.write( "Random winning #'s: 30,-20
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\n" ); document.write( "E(x) = (1/55)(30)+(54/55)(-20)
\n" ); document.write( "= (30-54*20)/55 = -1050/55
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\n" ); document.write( "= -$19.09
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\n" ); document.write( "All the competitors are contributing
\n" ); document.write( "$19.09 to the organizers.
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\n" ); document.write( "For a fair price the price to compete should be $x.
\n" ); document.write( "The Random winnings would be 50-x, -x
\n" ); document.write( "---
\n" ); document.write( "Expected winnings would be zero.
\n" ); document.write( "E(x) = (1/55)(50-x)+(54/55)(-x) = 0
\n" ); document.write( "---
\n" ); document.write( "[50-x-54x)/55 = 0
\n" ); document.write( "-55x+50 = 0
\n" ); document.write( "x = 50/55
\n" ); document.write( "x = $0.91
\n" ); document.write( "Each runner should pay 91 cents to compete.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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