document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=838663>Question 838663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there,\r<BR>\n" );
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document.write( "I am trying to work out the following:  52 card deck without replacement. 4 players 1 card each. First player has a heart. Each of the other 3 players get a card. What are the chances of ANY of the other 3 cards being a heart (or how do you work it out). <BR>\n" );
document.write( "This was where I got to: Second player: probability is 12/51 (twelve hearts left with 51 cards), Third player 12/50, Fourth 12/49. How do I determine the probability of ANY of the other players having a HEART? <BR>\n" );
document.write( "What do I do with these numbers - 0.2352941176470588, .24,<BR>\n" );
document.write( "0.2448979591836735  ?<BR>\n" );
document.write( "If I wanted to find out what was the probability of them ALL being HEARTS I would multiply these numbers (I think)\r<BR>\n" );
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document.write( "Would you recommend any text book / accessible material on this type of probability question?\r<BR>\n" );
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document.write( "Thanking you in advance\r<BR>\n" );
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document.write( "Kyran  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505187 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 52 cards, 13 Hearts, 39 Non-Hearts<BR>\n" );
document.write( "First player - Heart<BR>\n" );
document.write( "51 cards, 12 Hearts, 39 Non-Hearts<BR>\n" );
document.write( "Look at the possible draws of the next three cards (H - heart, N - non-heart) and calculate the probabilities of each, they are all independent events.<BR>\n" );
document.write( "NNN-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839%2F51%29%2838%2F50%29%2837%2F49%29=.438848 ALIGN=MIDDLE  ALT=\"%2839%2F51%29%2838%2F50%29%2837%2F49%29=.438848\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "NNH-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839%2F51%29%2838%2F50%29%2812%2F49%29=0.142329 ALIGN=MIDDLE  ALT=\"%2839%2F51%29%2838%2F50%29%2812%2F49%29=0.142329\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "NHN-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839%2F51%29%2812%2F50%29%2838%2F49%29=0.142329 ALIGN=MIDDLE  ALT=\"%2839%2F51%29%2812%2F50%29%2838%2F49%29=0.142329\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "NHH-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839%2F51%29%2812%2F50%29%2811%2F49%29=0.0412 ALIGN=MIDDLE  ALT=\"%2839%2F51%29%2812%2F50%29%2811%2F49%29=0.0412\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "HNN-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F51%29%2839%2F50%29%2838%2F49%29=0.142329 ALIGN=MIDDLE  ALT=\"%2812%2F51%29%2839%2F50%29%2838%2F49%29=0.142329\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "HNH-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F51%29%2839%2F50%29%2811%2F49%29=0.0412 ALIGN=MIDDLE  ALT=\"%2812%2F51%29%2839%2F50%29%2811%2F49%29=0.0412\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "HHN-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F51%29%2811%2F50%29%2839%2F49%29=0.0412 ALIGN=MIDDLE  ALT=\"%2812%2F51%29%2811%2F50%29%2839%2F49%29=0.0412\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "HHH-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F51%29%2811%2F50%29%2810%2F49%290.010564 ALIGN=MIDDLE  ALT=\"%2812%2F51%29%2811%2F50%29%2810%2F49%290.010564\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you sum up all of the probabilities, they do add up to 1. They must, these are the only possible draws.<BR>\n" );
document.write( "Now look for the ones that have at least 1 heart. <BR>\n" );
document.write( "Or look for the one that has no hearts and subtract from 1.<BR>\n" );
document.write( "P(at least 1 heart)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.438848=0.561152 ALIGN=MIDDLE  ALT=\"1-0.438848=0.561152\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Yes, all of them being hearts would be HHH, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=0.010564 ALIGN=MIDDLE  ALT=\"P=0.010564\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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