document.write( "Question 283185: Pick a card: Mike and Dave play the following game. Mike picks a card from a deck of cards. If he selects a heart, Dave gives him $5. If not, he gives Dave $2.\r
\n" ); document.write( "\n" ); document.write( "a) Determine Mike’s expectation
\n" ); document.write( "b) Determine Dave’s expectation.\r
\n" ); document.write( "\n" ); document.write( "I am completely lost. I know there are 52 cards in a deck and I know that of that, 13 are hearts. But I am lost as to where to go after that.\r
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Algebra.Com's Answer #205647 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Pick a card: Mike and Dave play the following game. Mike picks a card from a deck of cards. If he selects a heart, Dave gives him $5. If not, he gives Dave $2.
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document.write( "Mike's net winnings are \r\n" );
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document.write( " +$5 if he selects a heart or -$2 if he doesn't select a heart\r\n" );
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document.write( "Mike's expectation = \r\n" );
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document.write( "(net winnings if he gets a heart)*(probability of getting a heart)\r\n" );
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document.write( "                   plus\r\n" );
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document.write( "(net winnings if he doesn't get a heart)*(prob of not getting a heart)\r\n" );
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document.write( "Probability of Mike getting a heart =  or \r\n" );
document.write( "Probability of Mike NOT getting a heart =  or \r\n" );
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document.write( "So,\r\n" );
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document.write( "Mike's expectation = \r\n" );
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document.write( "If they continue to play the game many times, in the end \r\n" );
document.write( "Mike will have averaged LOSING 25 cents per game.\r\n" );
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document.write( "----------------------------\r\n" );
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document.write( "Dave's net winnings are \r\n" );
document.write( "\r\n" );
document.write( " -$5 if Mike selects a heart or +$2 if he doesn't select a heart\r\n" );
document.write( "\r\n" );
document.write( "Dave's expectation = \r\n" );
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document.write( "(net winnings if Mike gets a heart)*(probability of Mike getting a heart)\r\n" );
document.write( "                    \r\n" );
document.write( "                   plus\r\n" );
document.write( "\r\n" );
document.write( "(net winnings if Mike doesn't get a heart)*(prob of Mike not getting a heart)\r\n" );
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document.write( "\r\n" );
document.write( "Probability of Mike getting a heart =  or \r\n" );
document.write( "Probability of Mike NOT getting a heart =  or \r\n" );
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document.write( "So,\r\n" );
document.write( "\r\n" );
document.write( "Dave's expectation = \r\n" );
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document.write( "If they continue to play the game many times, in the end \r\n" );
document.write( "Dave will have averaged WINNING 25 cents per game.\r\n" );
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document.write( "Edwin

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