document.write( "Question 1201610: Kevin has a bag with 8 balls numbered 1 through 8. He is playing a game of chance.
\n" ); document.write( "This game is this: Kevin chooses one ball from the bag at random. He wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. He loses $16 if 7 or 8 is selected.\r
\n" ); document.write( "\n" ); document.write( "(If necessary, consult a list of formulas.)\r
\n" ); document.write( "\n" ); document.write( "(a.) Find the expected value of playing the game.\r
\n" ); document.write( "\n" ); document.write( "(b.) What can Kevin expect in the long run, after playing the game many times?
\n" ); document.write( "(He replaces the ball in the bag each time.) \n" ); document.write( "

Algebra.Com's Answer #836069 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Kevin has a bag with 8 balls numbered 1 through 8. He is playing a game of chance.
\n" ); document.write( "This game is this: Kevin chooses one ball from the bag at random. He wins $1 if the number 1 is selected,
\n" ); document.write( "$2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected,
\n" ); document.write( "$8 if the number 5 is selected, and $10 if the number 6 is selected. He loses $16 if 7 or 8 is selected.
\n" ); document.write( "(If necessary, consult a list of formulas.)
\n" ); document.write( "(a) Find the expected value of playing the game.
\n" ); document.write( "(b) What can Kevin expect in the long run, after playing the game many times?
\n" ); document.write( "(He replaces the ball in the bag each time.)
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document.write( "(a)  The expected value of playing the game is\r\n" );
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document.write( "          = 0  dollars.\r\n" );
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document.write( "     If you need more explanations, learn the definition of an expected value from your textbook\r\n" );
document.write( "     or other source.  It is the pre-requisite knowledge for this problem.\r\n" );
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document.write( "(b)  In the long run, Kevin may expect that his average value (win or lose) will be close to zero.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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