document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201400>Question 1201400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cards are drawn from a standard deck of cards. Find each probability\r<BR>\n" );
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document.write( "P(both kings or both black cards) \r<BR>\n" );
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document.write( "P(both face cards or both red)  </SPAN>\n" );
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document.write( "Problem 1<BR>\n" );
document.write( "P(both kings or both black cards) \r<BR>\n" );
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document.write( "There are 4 kings<BR>\n" );
document.write( "There are 52 cards total<BR>\n" );
document.write( "4/52 = 1/13 = probability of getting a king<BR>\n" );
document.write( "Assuming the card is not put back (aka no replacement), then<BR>\n" );
document.write( "4-1 = 3 kings left<BR>\n" );
document.write( "52-1 = 51 cards left<BR>\n" );
document.write( "3/51 = 1/17 = probability of getting another king, no replacement<BR>\n" );
document.write( "P(2 kings) = P(1st king)*P(2nd king)<BR>\n" );
document.write( "P(2 kings) = (4/52)*(3/51)<BR>\n" );
document.write( "P(2 kings) = (1/13)*(1/17)<BR>\n" );
document.write( "P(2 kings) = 1/221\r<BR>\n" );
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document.write( "26 black cards (13 spades + 13 clubs)<BR>\n" );
document.write( "52 cards total<BR>\n" );
document.write( "26/52 = 1/2 = probability of getting a black card<BR>\n" );
document.write( "26-1 = 25 black cards left<BR>\n" );
document.write( "52-1 = 51 cards left<BR>\n" );
document.write( "25/51 = probability of getting another black card, no replacement<BR>\n" );
document.write( "P(2 black cards) = P(1st black card)*P(2nd black card)<BR>\n" );
document.write( "P(2 black cards) = (26/52)*(25/51)<BR>\n" );
document.write( "P(2 black cards) = (1/2)*(25/51)<BR>\n" );
document.write( "P(2 black cards) = 25/102\r<BR>\n" );
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document.write( "2 black kings<BR>\n" );
document.write( "52 cards total<BR>\n" );
document.write( "P(2 black kings) = P(1st black king)*P(2nd black king)<BR>\n" );
document.write( "P(2 black kings) = (2/52)*(1/51)<BR>\n" );
document.write( "P(2 black kings) = 1/1326\r<BR>\n" );
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document.write( "P(2 kings or 2 black) = P(2 kings) + P(2 black) - P(2 black kings)<BR>\n" );
document.write( "P(2 kings or 2 black) = 1/221  +  25/102  -  1/1326<BR>\n" );
document.write( "P(2 kings or 2 black) = 6/1326 + 325/1326 - 1/1326<BR>\n" );
document.write( "P(2 kings or 2 black) = (6 + 325 - 1)/1326<BR>\n" );
document.write( "P(2 kings or 2 black) = 330/1326<BR>\n" );
document.write( "P(2 kings or 2 black) = (6*55)/(6*221)<BR>\n" );
document.write( "P(2 kings or 2 black) = <font color=red>55/221</font>\r<BR>\n" );
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document.write( "=====================================================\r<BR>\n" );
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document.write( "Problem 2<BR>\n" );
document.write( "P(both face cards or both red)\r<BR>\n" );
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document.write( "face cards = Jack, Queen, King<BR>\n" );
document.write( "3 face cards in any given suit<BR>\n" );
document.write( "4*3 = 12 face cards in the deck\r<BR>\n" );
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document.write( "P(2 face cards) = P(1st face card)P*(2nd face card)<BR>\n" );
document.write( "P(2 face cards) = (12/52)*(11/51)<BR>\n" );
document.write( "P(2 face cards) = (3/13)*(11/51)<BR>\n" );
document.write( "P(2 face cards) = 11/221<BR>\n" );
document.write( "I'm assuming that we are not replacing the 1st card.\r<BR>\n" );
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document.write( "26 red cards (13 hearts + 13 diamonds)<BR>\n" );
document.write( "P(2 red cards) = P(1st red card)*P(2nd red card)<BR>\n" );
document.write( "P(2 red cards) = (26/52)*(25/51)<BR>\n" );
document.write( "P(2 red cards) = (1/2)*(25/51)<BR>\n" );
document.write( "P(2 red cards) = 25/102\r<BR>\n" );
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document.write( "6 cards are red and a face card (eg: King of Diamonds)<BR>\n" );
document.write( "P(2 red face cards) = P(1st red face)*P(2nd red face)<BR>\n" );
document.write( "P(2 red face cards) = (6/52)*(5/51)<BR>\n" );
document.write( "P(2 red face cards) = (3/26)*(5/51)<BR>\n" );
document.write( "P(2 red face cards) = 15/1326<BR>\n" );
document.write( "P(2 red face cards) = 5/442\r<BR>\n" );
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document.write( "P(2 face or 2 red) = P(2 face) + P(2 red) - P(2 red face)<BR>\n" );
document.write( "P(2 face or 2 red) = 11/221  +  25/102  -  5/442<BR>\n" );
document.write( "P(2 face or 2 red) = 66/1326 + 325/1326 - 15/1326<BR>\n" );
document.write( "P(2 face or 2 red) = (66 + 325 - 15)/1326<BR>\n" );
document.write( "P(2 face or 2 red) = 376/1326<BR>\n" );
document.write( "P(2 face or 2 red) = (2*188)/(2*663)<BR>\n" );
document.write( "P(2 face or 2 red) = <font color=red>188/663</font>\r<BR>\n" );
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document.write( "Summary\r<BR>\n" );
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document.write( "P(both kings or both black cards) = <font color=red>55/221</font><BR>\n" );
document.write( "P(both face cards or both red) = <font color=red>188/663</font>\r<BR>\n" );
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document.write( "The 1st card wasn't put back, aka no replacement.<BR>\n" );
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