document.write( "Question 1148294: A poker hand consisting of 4 cards is dealt from a standard deck of 52 cards.
\n" ); document.write( "Find the probability that the hand contains exactly 2 face cards. \n" ); document.write( "

Algebra.Com's Answer #769719 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
A poker hand consisting of 4 cards is dealt from a standard deck of 52 cards.
\n" ); document.write( "Find the probability that the hand contains exactly 2 face cards.
\n" ); document.write( "

 \r\n" );
document.write( "There are 4 Kings, 4 Queens, and 4 Jacks in a standard 52-card deck.  That's 12\r\n" );
document.write( "face cards.  The other 52-12 = 40 cards are non-face cards.\r\n" );
document.write( "\r\n" );
document.write( "First we find the total number of possible 'successful' card-hands, i.e., those\r\n" );
document.write( "that contain exactly 2 face cards (and therefore exactly 2 non-face cards).\r\n" );
document.write( "\r\n" );
document.write( "The number of pairs of face cards are:\r\n" );
document.write( "\r\n" );
document.write( "12 face cards CHOOSE 2 = 12C2 = (12∙11)/(2∙1) = 66 ways\r\n" );
document.write( "\r\n" );
document.write( "The number of pairs of non-face cards are:\r\n" );
document.write( "\r\n" );
document.write( "That's 40 non-face cards CHOOSE 2 = 40C2 = (40∙39)/(2∙1) = 780 ways\r\n" );
document.write( "\r\n" );
document.write( "For each of the 66 ways to choose two face cards, there are 780 wats to choose\r\n" );
document.write( "two non-face cards to put with them to make a 'successful' 4-card hand\r\n" );
document.write( "\r\n" );
document.write( "That's 66∙780 = 51480 successful 4-card hands.\r\n" );
document.write( "\r\n" );
document.write( "Next we find the total number of 4-card hands, 'successful' ones and 'failures'\r\n" );
document.write( "together.\r\n" );
document.write( "\r\n" );
document.write( "That's 52 cards CHOOSE 4 = 52C4 = (52∙51∙50∙49)/(4*3*2*1) = 270725 possible \r\n" );
document.write( "4-card hands.\r\n" );
document.write( "\r\n" );
document.write( "So the probability is 51480/270725 = 0.1901560624\r\n" );
document.write( "\r\n" );
document.write( "Answer:  Very nearly 19% of the time you'll be dealt a hand that contains\r\n" );
document.write( "exactly 2 face cards and exactly 2 non-face cards.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );