Algebra.Com's Answer #814280 by ikleyn(52765)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Two  persons A and B are to draw alternately one ball at a time from an urn containing 3 white and 2 black balls,
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document.write( "drawn balls not being replaced. If A takes the first turn, what is the probability that A will be the first to draw white ?
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document.write( "We may think about the space of events as all possible sequences of the letters W and B of the length 5.\r\n" );
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document.write( "There are 120 permutations of 5 items; but if we consider the distinguishable arrangements of these sequences,\r\n" );
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document.write( "we have only  =  =  = 10 distinguishable orderings, so the space of events has 10 elements.\r\n" );
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document.write( "Next, the \"favorable\" arrangements are those that EITHER start from W (and then A takes white ball first),\r\n" );
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document.write( "OR those that start from BBW (and then there is only one such sequence BBWWW, where, again, A takes white ball first).\r\n" );
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document.write( "The number of distinguishable sequences W _ _ _ _ is  =  = 6.\r\n" );
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document.write( "The sequence BBWWW is a unique of that kind.\r\n" );
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document.write( "So, the number of favorable distinguishable sequences is (6+1) = 7, and the total space of events has 10 elements.\r\n" );
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document.write( "THEREFORE, the probability under the problem's question is P =  =  = 0.7 = 70%. ANSWER\r\n" );
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document.write( "Solved.\r
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document.write( "Good problem (!)\r
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document.write( "I like it (!)\r
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