document.write( "Question 129457: Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
\n" ); document.write( " a.) What is the probability that none of the 3 cards picked in this way is a face card?
\n" ); document.write( " b.) what is the probability that exactly one of the three cards picked is a face card? \n" ); document.write( "

Algebra.Com's Answer #94561 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Suppose that you take all of the black cards out of a standard deck of 52 cards
\n" ); document.write( "and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red
\n" ); document.write( "cards you will select 3 cards, one at a time, WITHOUT replacement, and record
\n" ); document.write( "weather each card is picked is a face card (a jack, queen, or king), or not a
\n" ); document.write( "face card.
\n" ); document.write( "

\r\n" );
document.write( "The sample space is\r\n" );
document.write( "\r\n" );
document.write( "AH,2H,3H,4H,5H,6H,7H,8H,9H,10H,JH,QH,KH\r\n" );
document.write( "AD,2D,3D,4D,5D,6D,7D,8D,9D,10D,JD,QD,KD\r\n" );
document.write( "\r\n" );
document.write( "It contains 6 face cards and 20 non-face cards.\r\n" );
document.write( "\r\n" );
document.write( "\"AND\" means \"multiply\"\r\n" );
document.write( "\"OR\" means \"add\".\r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "a.) What is the probability that none of the 3 cards picked in this way is a
\n" ); document.write( "face card?
\n" ); document.write( "

\r\n" );
document.write( "P(picking a non-face card first AND a non-face card second AND a non-face card\r\n" );
document.write( "  third) =\r\n" );
document.write( "\r\n" );
document.write( "P(picking a non-face card first) x P(picking a non-face card second) x\r\n" );
document.write( "P(picking a non-face card third) =\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "b.) what is the probability that exactly one of the three cards picked is a
\n" ); document.write( "face card?
\n" ); document.write( "

\r\n" );
document.write( "P[(face card 1st AND non-face card 2nd AND non-face card 3rd) OR\r\n" );
document.write( "  (non-face card 1st AND face card 2nd AND non-face card 3rd) OR\r\n" );
document.write( "  (non-face card 1st AND non-face card 2nd AND face card 3rd)] =\r\n" );
document.write( "\r\n" );
document.write( "P(face card 1st) x P(non-face card 2nd) x P(non-face card 3rd) +\r\n" );
document.write( "P(non-face card 1st) x P(face card 2nd) x P(non-face card 3rd) +\r\n" );
document.write( "P(non-face card 1st) x P(non-face card 2nd) x P(face card 3rd) =\r\n" );
document.write( "\r\n" );
document.write( " =\r\n" );
document.write( "\r\n" );
document.write( "= \r\n" );
document.write( "  \r\n" );
document.write( "------------------------\r\n" );
document.write( "\r\n" );
document.write( "Notice that the two answers happened to come out the same.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );