document.write( "Question 150573This question is from textbook a survey of mathematic with applications
\n" ); document.write( ": How would you put this in expected value and fair price of ticket?\r
\n" ); document.write( "\n" ); document.write( "1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded – one for $400, one for $200, and five for $50. Steven purchases one of the tickets. (Give solutions as decimals accurate to the nearest hundredth.)
\n" ); document.write( "a) Find the expected value
\n" ); document.write( "b) Find the fair price of the ticket. \r
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Algebra.Com's Answer #110604 by Edwin McCravy(20056) $\"\"$ $\"About$

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How would you put this in expected value and fair price of ticket?\r
\n" ); document.write( "\n" ); document.write( "1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded – one for $400, one for $200, and five for $50. Steven purchases one of the tickets. (Give solutions as decimals accurate to the nearest hundredth.)
\n" ); document.write( "a) Find the expected value
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document.write( "Note that we include -$2 as a \"negative prize\" in the likelihood that \r\n" );
document.write( "Steven doesn't win at all and loses his $2.  \r\n" );
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document.write( "Prizes  | Probability |  Expectation\r\n" );
document.write( " $398   |     .001    |      $0.398\r\n" );
document.write( " $198   |     .001    |      $0.198\r\n" );
document.write( " $ 48   |     .001    |      $0.048\r\n" );
document.write( " $ 48   |     .001    |      $0.048\r\n" );
document.write( " $ 48   |     .001    |      $0.048\r\n" );
document.write( " $ 48   |     .001    |      $0.048\r\n" );
document.write( " $ 48   |     .001    |      $0.048\r\n" );
document.write( " $ -2   |     .993    |     -$1.986\r\n" );
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document.write( "Total expectation =         -$1.15 \r\n" );
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document.write( "The expected value is -$1.15 or a LOSS of $1.15\r\n" );
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document.write( "That is, if this raffle were held every week, and Steven\r\n" );
document.write( "played it every time, he would average losing $1.15 per\r\n" );
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document.write( "b) Find the fair price of the ticket\r\n" );
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document.write( "The easiest way to do this problem is just to pretend that\r\n" );
document.write( "they give him his ticket price back in the problem above.  \r\n" );
document.write( "So we then just add $2 to the -$1.15 and get $2 - $1.15 = $0.85.  \r\n" );
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document.write( "But to work it out: \r\n" );
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document.write( "Let the fair price be $x\r\n" );
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document.write( "We put -x where we put -2 above and\r\n" );
document.write( "-.993x for the expectation, and 0 for\r\n" );
document.write( "the Total expectation:\r\n" );
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document.write( "Prizes    | Probability |  Expectation\r\n" );
document.write( " $400-x   |     .001    |      $0.40-.001x\r\n" );
document.write( " $200-x   |     .001    |      $0.20-.001x\r\n" );
document.write( " $ 50-x   |     .001    |      $0.05-.001x\r\n" );
document.write( " $ 50-x   |     .001    |      $0.05-.001x\r\n" );
document.write( " $ 50-x   |     .001    |      $0.05-.001x\r\n" );
document.write( " $ 50-x   |     .001    |      $0.05-.001x\r\n" );
document.write( " $ 50-x   |     .001    |      $0.05-.001x\r\n" );
document.write( " $ -x     |     .993    |     -$0.993x\r\n" );
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document.write( "Total expectation =             $0.000 \r\n" );
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document.write( "Add the right column and make an equation:\r\n" );
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document.write( "                         0.85 - x = 0\r\n" );
document.write( "                             0.85 = x   \r\n" );
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document.write( "That is, if this raffle were held every week, and the price were\r\n" );
document.write( "85 cents, and Steven played it every time, he would average \r\n" );
document.write( "breaking even.  That fair ticket price is 85 cents. \r\n" );
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document.write( "Edwin

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