document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161243>Question 1161243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I draw a card from a standard 52-card deck. If I draw an Ace, I win 1 dollar. If I draw a 2 through 10, I win a number of dollars equal to the value of the card. If I draw a face card (Jack, Queen, or King), I win 20 dollars. If I draw a $\clubsuit$, my winnings are doubled, and if I draw a $\spadesuit$, my winnings are tripled. (For example, if I draw the $8\clubsuit$, then I win 16 dollars.) What would be a fair price to pay to play the game? Express your answer as a dollar value rounded to the nearest cent.\r<BR>\n" );
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document.write( "Your answer should be a number with two digits after the decimal point, like $21.43$.<BR>\n" );
document.write( "EXPECTED VALUE QUESTION<BR>\n" );
document.write( "I would appreciate any help<BR>\n" );
document.write( "This is expected value. So for the ace, it would be E = (1) 4/52 as a decimal(.923076923) and for the face cards it would be (12/52 ) as a decimal ??(20) so it would be E= (1)(923076923) + (20)(0.230769231) the rest i don't know, please help<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784748 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=784748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "If you draw a red Ace, you get $1.  There are 2 red aces in the deck, so the probability of drawing a red Ace is 1/26.  The expected value of drawing a red ace is then (1/26)(1) which is approximately $0.04.\r<BR>\n" );
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document.write( "The club Ace gets you $2, 1 club ace, 1/52 times $2 is the same $0.04.\r<BR>\n" );
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document.write( "The spade Ace is worth $3, 1/52 times $3 gives E(AS) = $0.06.\r<BR>\n" );
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document.write( "For the 2s, you have 2 times 1/26, 4 times 1/52, and 6 times 1/52.\r<BR>\n" );
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document.write( "The rest are summarized in the following table:\r<BR>\n" );
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document.write( " A♥♦	 1	  1/26	 $0.04 \r\n" );
document.write( " A ♣	 2	  1/52	 $0.04 \r\n" );
document.write( " A ♠	 3	  1/52	 $0.06 \r\n" );
document.write( " 2♥♦	 2	  1/26	 $0.08 \r\n" );
document.write( " 2 ♣	 4	  1/52	 $0.08 \r\n" );
document.write( " 2 ♠	 6	  1/52	 $0.12 \r\n" );
document.write( " 3♥♦	 3	  1/26	 $0.12 \r\n" );
document.write( " 3 ♣	 6	  1/52	 $0.12 \r\n" );
document.write( " 3 ♠	 9	  1/52	 $0.17 \r\n" );
document.write( " 4♥♦	 4	  1/26	 $0.15 \r\n" );
document.write( " 4 ♣	 8	  1/52	 $0.15 \r\n" );
document.write( " 4 ♠	12	  1/52	 $0.23 \r\n" );
document.write( " 5♥♦	 5	  1/26	 $0.19 \r\n" );
document.write( " 5 ♣	10	  1/52	 $0.19 \r\n" );
document.write( " 5 ♠	15	  1/52	 $0.29 \r\n" );
document.write( " 6♥♦	 6	  1/26	 $0.23 \r\n" );
document.write( " 6 ♣	12	  1/52	 $0.23 \r\n" );
document.write( " 6 ♠	18	  1/52	 $0.35 \r\n" );
document.write( " 7♥♦	 7	  1/26	 $0.27 \r\n" );
document.write( " 7 ♣	14	  1/52	 $0.27 \r\n" );
document.write( " 7 ♠	21	  1/52	 $0.40 \r\n" );
document.write( " 8♥♦	 8	  1/26	 $0.31 \r\n" );
document.write( " 8 ♣	16	  1/52	 $0.31 \r\n" );
document.write( " 8 ♠	24	  1/52	 $0.46 \r\n" );
document.write( " 9♥♦	 9	  1/26	 $0.35 \r\n" );
document.write( " 9 ♣	18	  1/52	 $0.35 \r\n" );
document.write( " 9 ♠	27	  1/52	 $0.52 \r\n" );
document.write( "10♥♦	10	  1/26	 $0.38 \r\n" );
document.write( "10 ♣	20	  1/52	 $0.38 \r\n" );
document.write( "10 ♠	30	  1/52	 $0.58 \r\n" );
document.write( " F♥♦	20	  3/26	 $2.31 \r\n" );
document.write( " F ♣	40	  3/52	 $2.31 \r\n" );
document.write( " F ♠	60	  3/52	 $3.46 \r\n" );
document.write( "			$15.48\r\n" );
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document.write( "The expected value of the game is the sum of the individual expected values.  By the way, don't add the numbers in the expected value column -- they are all rounded and you will get an incorrect sum.  The correct sum of the unrounded values which is then rounded to two digits is shown.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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