document.write( "Question 201488: Consider a standard deck of playing cards (52 cards, no jokers). If you draw two cards, what is the probability that the cards are:
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\n" ); document.write( "b. two kings?
\n" ); document.write( "c. two mismatched cards (do not share suit or face value)?
\n" ); document.write( "d. two queens?
\n" ); document.write( "e. any pair (same face value)?
\n" ); document.write( "f. two matching cards (have either same suit or same face value)?\r
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Algebra.Com's Answer #151696 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Consider a standard deck of playing cards (52 cards, no jokers). If you draw two cards, what is the probability that the cards are:
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document.write( "13 spades, choose 2     13C2      78       1\r\n" );
document.write( "------------------- =  ------ =  ---- =  ----- = .0588235294\r\n" );
document.write( "52 cards, choose 2      52C2     1326     17\r\n" );
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\n" ); document.write( "b. two kings?
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document.write( "4 kings, CHOOSE 2        4C2       6       1\r\n" );
document.write( "------------------- =  ------ =  ---- =  ----- = .0045248869\r\n" );
document.write( "52 cards, CHOOSE 2      52C2     1326     221\r\n" );
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\n" ); document.write( "c. two mismatched cards (do not share suit or face value)?
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document.write( "(4 suits CHOOSE 2) and (13 face values POSITION 2)\r\n" );
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document.write( "For instance if you chose the 2 suits as clubs and hearts, and then picked \r\n" );
document.write( "7 and queen for the face values, then you have to POSITION those on the\r\n" );
document.write( "clubs or hearts,  For you could either have the 7 of clubs and the queen of\r\n" );
document.write( "hearts, where you have POSITIONed them one way, or the 7 of hearts and the\r\n" );
document.write( "queen of clubs where you POSITION them another way. \r\n" );
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document.write( "\"And\" means \"multiply\".  So, we have\r\n" );
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document.write( "(4C2)(13P2)   (6)(156)     12\r\n" );
document.write( "----------- = --------- = ---- = .7058823529\r\n" );
document.write( "  C(52,2)       1326       17 \r\n" );
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\n" ); document.write( "d. two queens?
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document.write( "That's just like b, 2 kings, above:\r\n" );
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document.write( "4 queens, CHOOSE 2       4C2       6       1\r\n" );
document.write( "------------------- =  ------ =  ---- =  ----- = .0045248869\r\n" );
document.write( "52 cards, CHOOSE 2      52C2     1326     221\r\n" );
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\n" ); document.write( "e. any pair (same face value)?
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document.write( "(13 face values CHOOSE 1) AND THEN (4 suits CHOOSE 2)\r\n" );
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document.write( "(13C1)(4C2)    (13)(6)    78      1\r\n" );
document.write( "----------- = -------- = ---- = ----\r\n" );
document.write( "   52C2         1326     1326    17\r\n" );
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\n" ); document.write( "f. two matching cards (have either same suit or same face value)?
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document.write( "We have to break that into two mutually exclusive cases\r\n" );
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document.write( "1.  Cases where they have the same suit but two different face values.\r\n" );
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document.write( "     (4 suits CHOOSE 1)x(13 face values CHOOSE 2) \r\n" );
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document.write( "     (4C1)(13C2) \r\n" );
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document.write( "2.  Cases where they have the same face value but two different suits.\r\n" );
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document.write( "     (13 face values CHOOSE 1)x(4 suits CHOOSE 2)\r\n" );
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document.write( "     (13C1)(4C2)\r\n" );
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document.write( "Since it's either case 1 OR case 2 we add.  [Often with OR you add;\r\n" );
document.write( "but with AND you multiply].  \r\n" );
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document.write( "     (4C1)(13C2)+(13C1)(4C2)    (4)(78)+(13)(6)     390      5  \r\n" );
document.write( "     ----------------------- = ---------------- = ------ = ----\r\n" );
document.write( "             52C2                    1326          1326     17\r\n" );
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document.write( "Edwin
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