document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206558>Question 1206558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails.<BR>\n" );
document.write( "•    	If the card is a face card, and the coin lands on Heads, you win $9<BR>\n" );
document.write( "•    	If the card is a face card, and the coin lands on Tails, you win $2<BR>\n" );
document.write( "•    	If the card is not a face card, you lose $2, no matter what the coin shows.<BR>\n" );
document.write( "Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844107 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it has been pointed out that my solution is wrong.<BR>\n" );
document.write( "i went back to see where i went wrong.<BR>\n" );
document.write( "i think i found it.<BR>\n" );
document.write( "the problem was not in the procedure.<BR>\n" );
document.write( "it was in the arithmetic.<BR>\n" );
document.write( "thanks to the other tutors who set me straight.<BR>\n" );
document.write( "my apologies to the student that i provided an incorrect solution to.\r<BR>\n" );
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document.write( "here is the corrected solution.\r<BR>\n" );
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document.write( "if the card is a face card and the coin lands on heads, you win 9.<BR>\n" );
document.write( "if the card is a face card and the coin lands on tails, you win 2.<BR>\n" );
document.write( "if the card is not a face card, you lose 2.\r<BR>\n" );
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document.write( "there are 12 face cards in the deck.<BR>\n" );
document.write( "4 jacks<BR>\n" );
document.write( "4 queens<BR>\n" );
document.write( "4 kinds\r<BR>\n" );
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document.write( "probability of getting a face card is 12/52.<BR>\n" );
document.write( "probability of a coin landing on heads is 1/2.<BR>\n" );
document.write( "probability of a coin landing on tails is 1/2.\r<BR>\n" );
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document.write( "probability of getting a face card and a coin landing on heads is 12/52 * 1/2 = 12/104 = 3/26.\r<BR>\n" );
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document.write( "probability of getting a face card and a coin landing on tails is 12/52 * 1/2 = 12/104 = 3/26.\r<BR>\n" );
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document.write( "probability of not landing on a face card is 40/52 = 20/26.\r<BR>\n" );
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document.write( "your expected value if you get a face card and flip heads is 9.<BR>\n" );
document.write( "your expected value if you get a face card and flip tails is 2.<BR>\n" );
document.write( "your expected value if you don't get a face card is -2.\r<BR>\n" );
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document.write( "your overall expected value is 3/26 * 9 + 3/26 * 2 - 20/26 * 2 = (27 + 6 - 40) / 26 = -7 / 26 = -.2692307692.\r<BR>\n" );
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document.write( "round to the nearest penny to get -.27.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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