document.write( "Question 1186751: I was dealt a hand in bridge yesterday that had all 4 aces and 4 kings in the same hand. What are the odds of that happening? \n" ); document.write( "

Algebra.Com's Answer #817723 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
I was dealt a hand in bridge yesterday that had all 4 aces and 4 kings in the
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document.write( "I wish people wouldn't use the word \"odds\" when they mean \"probability\", which\r\n" );
document.write( "is what was meant in all probability. lol.  If they are going to use \"odds\",\r\n" );
document.write( "they should say \"odds in favor\" or \"odds against\", neither of which is the same\r\n" );
document.write( "as probability.\r\n" );
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document.write( "A bridge hand consists of 13 cards. So there are 5 cards besides the 4 aces and\r\n" );
document.write( "4 kings.  They are chosen from the other 52-8=44 cards, so there are\r\n" );
document.write( "C(44,5)=1086008 ways that could happen.\r\n" );
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document.write( "The number of ways that any 13 cards could have been dealt is\r\n" );
document.write( "C(52,13)=635013559600\r\n" );
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document.write( "So the probability of that happening is 1086008/635013559600 which reduces to\r\n" );
document.write( "11/6431950, about 0.0000017\r\n" );
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document.write( "That means that on the average, you'll get such a hand only 11 times out of\r\n" );
document.write( "every 6431950 times you are dealt a hand.  That's what \"probability\" means.\r\n" );
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document.write( "Now since you mentioned \"odds\", we must calculate how many times you will fail\r\n" );
document.write( "to get such a hand. \r\n" );
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document.write( "Since on the average, you'll get such a hand only 11 times out of every 6431950\r\n" );
document.write( "times you are dealt a hand, then\r\n" );
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document.write( "on the average, you'll FAIL TO get such a hand a whopping 6431939 times out of every \r\n" );
document.write( "6431950 times you are dealt a hand. \r\n" );
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document.write( "So your odds IN FAVOR OF getting such a hand is the ratio of 11 to 6431939, or\r\n" );
document.write( "about 1 to 584721, often written with a colon 1:58471).\r\n" );
document.write( "('Odds in favor' are usually given approximately as \"1 in 'some number'\".)\r\n" );
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document.write( "Your odds AGAINST getting such a hand is the ratio of 6431939 to 11, or about\r\n" );
document.write( "584721 to 1, also often written with a colon 58471:1).\r\n" );
document.write( "('Odds against' are usually given approximately as \"'some number' to 1\".)\r\n" );
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document.write( "So \r\n" );
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document.write( "and\r\n" );
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document.write( " usually approximated by dividing both numbers by \r\n" );
document.write( "the number of SUCCESSES to make the first number in the ratio 1.\r\n" );
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document.write( " usually\r\n" );
document.write( "approximated by dividing both numbers by the number of SUCCESSES to make the\r\n" );
document.write( "second number in the ratio 1.\r\n" );
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document.write( "Now you know why I said what I said above about the word \"odds\". lol\r\n" );
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document.write( "ALSO, if you actually were dealt all 4 aces and all 4 kings, it is most likely\r\n" );
document.write( "that the cards were not shuffled well after some card game that put them\r\n" );
document.write( "together.\r\n" );
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document.write( "Edwin

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