document.write( "Question 588395: A 13-card hand is dealt from a standard deck of 52 cards. What is
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Algebra.Com's Answer #374504 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
A 13-card hand is dealt from a standard deck of 52 cards. What is
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document.write( "P(no spades|exactly 5 hearts) =\r\n" );
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document.write( "P(no spades and exactly 5 hearts)\r\n" );
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document.write( "     P(exactly 5 hearts)\r\n" );
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document.write( "N(no spades and exactly 5 hearts)/C(52,13)\r\n" );
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document.write( "     N(exactly 5 hearts)/C(52,13)\r\n" );
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document.write( "Multiply top and bottom by C(52,13)\r\n" );
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document.write( "N(no spades and exactly 5 hearts)\r\n" );
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document.write( "      N(exactly 5 hearts) \r\n" );
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document.write( "N(no spades and exactly 5 hearts) =\r\n" );
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document.write( "(The number of ways to pick 8 from the 26 non-spades-non-hearts) \r\n" );
document.write( "times \r\n" );
document.write( "(the number of ways to pick exactly 5 hearts from the 13) = \r\n" );
document.write( "C(26,8)·C(13,5)\r\n" );
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document.write( "N(8 non-hearts and exactly 5 hearts) =\r\n" );
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document.write( "(The number of ways to pick 8 nun-hearts from 39 non-hearts) \r\n" );
document.write( "times \r\n" );
document.write( "(the number of ways to pick exactly 8 hearts from the 13) =\r\n" );
document.write( "C(39,8)·C(13,5)\r\n" );
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document.write( "Therefore,\r\n" );
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document.write( "P(no spades|exactly 5 hearts) = \r\n" );
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document.write( "C(26,8)·C(13,5)    C(26,8)\r\n" );
document.write( "--------------- =  ------- = .0253930401\r\n" );
document.write( "C(39,8)·C(13,5)    C(39,8) \r\n" );
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document.write( "That is the probability of the complement event of part (a), so it's\r\n" );
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document.write( "1 - .0253930401 = .9746069599\r\n" );
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document.write( "Edwin
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