document.write( "Question 1177054: A and B plays 12 games of chess of which 6 are won by A, 4 are won by B and two ends on a tie. They agree to play a tournament consistian of 3 games. Find the probability that A wins all three games. \n" ); document.write( "

Algebra.Com's Answer #805265 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "A and B plays 12 games of chess of which 6 are wonby A, 4 are won by B and two ends on a tie.
\n" ); document.write( "They agree to play a tournament $\"highlight%28cross%28consistian%29%29\"$ CONSISTING of 3 games.
\n" ); document.write( "Find the probability that A wins all three games.
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\n" ); document.write( "\n" ); document.write( "This problem is, actually, a standard problem of this class, but expressed in slightly unusual terms,
\n" ); document.write( "which may create difficulties to you in understanding its meaning.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, I will re-formulate this problem EQUIVALENTLY in familiar terms.\r
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document.write( "    +------------------------------------------------------------------------+\r\n" );
document.write( "    |   In a bag, there are 6 black balls, 4 white balls and 2 blue balls.   |\r\n" );
document.write( "    |   You draw 3 of these balls randomly without replacement.              |  \r\n" );
document.write( "    |   What is the probability to draw 3 black balls ?                      |\r\n" );
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\n" ); document.write( "\n" ); document.write( "SOLUTION\r
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document.write( "The probability to win the first of the 3 games is  P(win 1st) =  = .\r\n" );
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document.write( "The probability to win the second of the 3 games is  P(win 2nd) = .\r\n" );
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document.write( "The probability to win the third of the 3 games is  P(win 1st) =  = .\r\n" );
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document.write( "The probability to win all 3 games is  \r\n" );
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document.write( "    P = P(win 1st)*P(win 2nd)*P(win 3rd) =  =  = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The solution by @ewatrrr is INCORRECT, and her interpretation of the problem is INCORRECT, too.\r
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\n" ); document.write( "\n" ); document.write( "So, ignore her post for your safety.\r
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