document.write( "Question 386643: You are playing go fish with a friend and you have the cards 7,7,5,5,2,an Ace and a King your friend has seven cards too and you are playing with a set of fifty two cards what is the probability that your friend has one of the cards in their hand that you have in yours? \n" ); document.write( "

Algebra.Com's Answer #273328 by Edwin McCravy(20060) $\"\"$ $\"About$

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You are playing go fish with a friend and you have the cards 7,7,5,5,2,an Ace and a King your friend has seven cards too and you are playing with a set of fifty two cards what is the probability that your friend has one of the cards in their hand that you have in yours?
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document.write( "We define the sample space which is the set of combinations of 7 cards\r\n" );
document.write( "from the 52-7 or 45 cards besides the 7 cards in your hand.  \r\n" );
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document.write( "So the denominator of your desired probability is 45C7 = 45379620\r\n" );
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document.write( "We will first find the probability of the complement event and then \r\n" );
document.write( "subtract its probability from 1.\r\n" );
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document.write( "The complement event is:\r\n" );
document.write( "\"Your friend's combination of 7 cards does not contain a seven, or a five, or\r\n" );
document.write( "a two, or an Ace, or a King. \r\n" );
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document.write( "Now among the 45 cards not in your hand, there are 2 sevens, 2 fives, 3 twos,\r\n" );
document.write( "3 Aces, and 3 Kings. That's 2+2+3+3+3 = 13 cards that match one of your cards,\r\n" );
document.write( "and therefore 45-13 or 32 which don't match any of your cards.\r\n" );
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document.write( "So in order for your friend not to have a seven or a five, or a two, or an Ace,\r\n" );
document.write( "or a King, your friend must have a combination of 7 cards from those remaining\r\n" );
document.write( "32 cards.\r\n" );
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document.write( "So there are 32C7 = 3365856 possible 7-card hands he or she could have from the\r\n" );
document.write( "32 cards that do not match any of the cards in your hand.\r\n" );
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document.write( "So the numerator of the probability of the complement event is\r\n" );
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document.write( "So the desired probability is 1 - .0741710927 = .9258289073.\r\n" );
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document.write( "So there's a 92.6% chance that your friend has some card of the same rank as\r\n" );
document.write( "one of yours.  That's pretty likely.\r\n" );
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document.write( "Edwin

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