document.write( "Question 1127159: Suppose a certain game is fair and costs $3 if you lose and has a net payoff of $7 if you win. The only possible outcomes of the game are winning and losing. What is the probability of winning? \n" ); document.write( "

Algebra.Com's Answer #743711 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let x be the probability of winning; then 1-x is the probability of losing.

\n" ); document.write( "The game is fair if the expected value is 0.

\n" ); document.write( "To find the expected value, find the product of each outcome and its probability and add the products.

\n" ); document.write( "There are two possible outcomes: win (value +7, probability x) or lose (value -3, probability (1-x))

\n" ); document.write( " $\"%28%2B7%29%28x%29%2B%28-3%29%281-x%29+=+0\"$
\n" ); document.write( " $\"7x-3%2B3x+=+0\"$
\n" ); document.write( " $\"10x+=+3\"$
\n" ); document.write( " $\"x+=+.3\"$

\n" ); document.write( "The probability of winning is 0.3, or 30%. \n" ); document.write( "

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