document.write( "Question 281388: Suppose that the following game is played. A woman rolls a fair die. If she rolls a 1 or 6, she loses $1. If she rolls a 2 or a 5, she loses $2. If she rolls a 3 or 4, she wins $9. What is the expected value of the game? \n" ); document.write( "
Algebra.Com's Answer #204392 by Mathematicians(84)\"\" \"About 
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I would first set up a table where P(x) is the probability for event x and the outcome if x happens (or Y). For example, your question would start like this. Some basic information is that a die has 6 sides, therefore a fair die has a probability of landing 1/6 on each side.\r
\n" ); document.write( "\n" ); document.write( "X -- P(x) -- Y
\n" ); document.write( "1 -- 1/6 -- -$1
\n" ); document.write( "2 -- 1/6 -- -$2
\n" ); document.write( "3 -- 1/6 -- +$9
\n" ); document.write( "4 -- 1/6 -- +$9
\n" ); document.write( "5 -- 1/6 -- -$2
\n" ); document.write( "6 -- 1/6 -- -$1\r
\n" ); document.write( "\n" ); document.write( "When you have a table like this, you want to multiply each P(x) * y and add them up.\r
\n" ); document.write( "\n" ); document.write( "So in your case we would get:\r
\n" ); document.write( "\n" ); document.write( " 1/6 * -$1
\n" ); document.write( "+1/6 * -$2
\n" ); document.write( "+1/6 * +$9
\n" ); document.write( "+1/6 * +$9
\n" ); document.write( "+1/6 * -$2
\n" ); document.write( "+1/6 * -$1\r
\n" ); document.write( "\n" ); document.write( "= $(-1/6 - 2/6 + 9/6 + 9/6 - 2/6 - 1/6) (It is helpful if you keep the same denominator)\r
\n" ); document.write( "\n" ); document.write( "= + $12/6 = $2\r
\n" ); document.write( "\n" ); document.write( "$2 is the expected value. What this represents is that if you somehow played infinite games, you would win an average of $2 per game. \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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