document.write( "Question 1151292: An urn contains 6 red balls and 3 blue balls. One ball is selected atrandom and is replaced by a ball of the other color. A second ball is thenchosen. What is the
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Algebra.Com's Answer #772989 by Edwin McCravy(20060)\"\" \"About 
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An urn contains 6 red balls and 3 blue balls. One ball is selected at random and
\n" ); document.write( "is replaced by a ball of the other color. A second ball is then chosen. What is
\n" ); document.write( "the conditional probability that the first ball selected is red, given that the
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document.write( "There are 4 possible cases RR, RB, BR, BB\r\n" );
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document.write( "Start with 6 reds and 3 blues.\r\n" );
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document.write( "Case 1: RR  The first one will be red about 6 times out of 9 or 6/9ths of the\r\n" );
document.write( "time, and after reducing to lowest terms, that's the same as 2/3rds of the time,\r\n" );
document.write( "or a probability of 2/3.\r\n" );
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document.write( "Then the red one drawn first will be removed and replaced, giving 1 less red\r\n" );
document.write( "balls and 1 more blue balls.  That'll be 5 reds and 4 blues.  That will happen 5\r\n" );
document.write( "times out of 9 times (when you've draw a red ball first).\r\n" );
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document.write( "So P(RR) = (2/3)(5/9) = 10/27 [10 times out of 27]\r\n" );
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document.write( "Case 2: RB  The first one will be red about 6 times out of 9 or 6/9ths of the\r\n" );
document.write( "time, and after reducing to lowest terms, that's the same as 2/3rds of the time,\r\n" );
document.write( "or a probability of 2/3.\r\n" );
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document.write( "Then the red one drawn first will be removed and replaced, giving 1 less red\r\n" );
document.write( "balls and 1 more blue balls.  That'll be 5 reds and 4 blues.  That will happen 4\r\n" );
document.write( "times out of 9 times (when you've draw a red ball first).\r\n" );
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document.write( "So P(RR) = (2/3)(4/9) = 8/27 [8 times out of 27]\r\n" );
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document.write( "Case 3: BR  The first one will be blue about 3 times out of 9 or 3/9ths of the\r\n" );
document.write( "time, and after reducing to lowest terms, that's the same as 1/3rd of the time,\r\n" );
document.write( "or a probability of 1/3.\r\n" );
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document.write( "Then the blue one drawn first will be removed and replaced by a red ball, giving\r\n" );
document.write( "1 more red balls and 1 less blue balls.  That'll be 7 reds and 2 blues. That\r\n" );
document.write( "will happen 7 times out of 9 times (when you've draw a blue ball first).\r\n" );
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document.write( "So P(BR) = (1/3)(7/9) = 7/27 [7 times out of 27]\r\n" );
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document.write( "Case 4: BB  The first one will be blue about 3 times out of 9 or 3/9ths of the\r\n" );
document.write( "time, and after reducing to lowest terms, that's the same as 1/3rd of the time,\r\n" );
document.write( "or a probability of 1/3.\r\n" );
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document.write( "Then the blue one drawn first will be removed and replaced by a red ball, giving\r\n" );
document.write( "1 more red balls and 1 less blue balls.  That'll be 7 reds and 2 blues.\r\n" );
document.write( "That will happen 2 times out of 9 times (when you've draw a blue ball first).\r\n" );
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document.write( "So P(BB) = (1/3)(2/9) = 2/27 [2 times out of 27]\r\n" );
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document.write( "We may use this tree diagram:\r\n" );
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document.write( "That equals\r\n" );
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document.write( "Edwin
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