document.write( "Question 697405: A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is (i)a card of spade or an ace (ii)a red king (iii)neither a king nor a queen (iv)either a king or queen.\r
\n" ); document.write( "\n" ); document.write( "Thank you. \n" ); document.write( "
Algebra.Com's Answer #430028 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is \r
\n" ); document.write( "\n" ); document.write( "(i)a card of spade or an ace
\n" ); document.write( "
\r\n" );
document.write( "This asks for the probability of drawing one of these 16\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "A♥   \r\n" );
document.write( "A♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  \r\n" );
document.write( "A♣   \r\n" );
document.write( "\r\n" );
document.write( "out of these 52:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ \r\n" );
document.write( "\r\n" );
document.write( "In probability theory \"out of\" means over, so \"16 out of 52\" means\r\n" );
document.write( "\"16 over 52\" and that is \"16%2F52\" and that reduces to \"4%2F13\"\r\n" );
document.write( "-------------------------------------------------------------------\r\n" );
document.write( "

\n" ); document.write( "(ii)a red king
\n" ); document.write( "
\r\n" );
document.write( "This asks for the probability of drawing one of these 2\r\n" );
document.write( "\r\n" );
document.write( "                                                        K♥ \r\n" );
document.write( "                                                        K♦\r\n" );
document.write( "out of these 52:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ \r\n" );
document.write( "\r\n" );
document.write( "In probability theory \"out of\" means over, so \"2 out of 52\" means\r\n" );
document.write( "\"2 over 52\" and that is \"2%2F52\" and that reduces to \"1%2F26\"\r\n" );
document.write( "------------------------------------------------------------------\r\n" );
document.write( "

\n" ); document.write( "(iii)neither a king nor a queen
\n" ); document.write( "
\r\n" );
document.write( "This asks for the probability of drawing one of these 44\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥   \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  \r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠    \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣   \r\n" );
document.write( "\r\n" );
document.write( "out of these 52:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ \r\n" );
document.write( "\r\n" );
document.write( "In probability theory \"out of\" means over, so \"44 out of 52\" means\r\n" );
document.write( "\"44 over 52\" and that is \"44%2F52\" and that reduces to \"11%2F13\" \r\n" );
document.write( "--------------------------------------------------------------------\r\n" );
document.write( "

\n" ); document.write( "(iv)either a king or queen.\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "This asks for the probability of drawing one of these 8\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "                                                    Q♥  K♥ \r\n" );
document.write( "                                                    Q♦  K♦\r\n" );
document.write( "                                                    Q♠  K♠  \r\n" );
document.write( "                                                    Q♣  K♣    \r\n" );
document.write( "\r\n" );
document.write( "out of these 52:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣\r\n" );
document.write( "\r\n" );
document.write( "In probability theory \"out of\" means over, so \"8 out of 52\" means\r\n" );
document.write( "\"2 over 52\" and that is \"8%2F52\" and that reduces to \"2%2F13\"\r\n" );
document.write( "------------------------------------------------------------------ \r\n" );
document.write( "Notice that (iii) and (iv) are complement events, so we could have\r\n" );
document.write( "gotten the answer to (iv) by subtracting the probability of (iii)\r\n" );
document.write( "from 1:\r\n" );
document.write( "\r\n" );
document.write( "1 - \"11%2F13\" = \"13%2F13\" - \"11%2F13%7D%7D+=+%7B%7B%7B2%2F13\".\r\n" );
document.write( "\r\n" );
document.write( "It would have been easier to have done (iv) first and then gotten the\r\n" );
document.write( "answer to (iii) by\r\n" );
document.write( "\r\n" );
document.write( "1 - \"2%2F13\" = \"13%2F13\" - \"2%2F13%7D%7D+=+%7B%7B%7B11%2F13\".\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );