document.write( "Question 443025: Essay. Show all work. A community 5k run will award $50 to the winner. 50 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 #305568 by stanbon(75887) $\"\"$ $\"About$

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A community 5k run will award $50 to the winner. 50 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( "---------------------------------------
\n" ); document.write( "Random gain values for the runners assuming they pay \"x\" to compete:
\n" ); document.write( "-x and 50-x
\n" ); document.write( "----
\n" ); document.write( "Corresponding probabilities:
\n" ); document.write( "(49/50) and (1/50)
\n" ); document.write( "-------
\n" ); document.write( "E(x) = (49/50)(-x)+(1/50)(50-x)
\n" ); document.write( "---
\n" ); document.write( "For the entry price to be \"fair\" E(x) must be zero.
\n" ); document.write( "----
\n" ); document.write( "Solve:
\n" ); document.write( "(49/50)(-x)+(1/50)(50-x)
\n" ); document.write( "[-49x+50-x]/50 = 0
\n" ); document.write( "-50x+50 = 0
\n" ); document.write( "x = $1.00
\n" ); document.write( "==================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

\n" );