Algebra.Com's Answer #844682 by ikleyn(52817)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "John was trying to bet Krista $100 that he could pick 7 people at random and at least two of them
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document.write( "would have a birthday in the same month. Krista did the math before making the bet and found that
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document.write( "there was the following chance of her winning the bet.
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document.write( "a. 11%
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document.write( "b. 89%
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document.write( "c. 4.6%
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document.write( "d. 95.4%
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document.write( "Consider 7 people A, B, C, D, E, F and G.\r\n" );
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document.write( "Person A has birthday in some of 12 months, X.\r\n" );
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document.write( "The probability that person B has birthday in some other month Y, different from X, is  .\r\n" );
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document.write( "The probability that person C has birthday in some other month Z, different from X and Y, is  .\r\n" );
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document.write( "The probability that person D has birthday in some other month W, different from X, Y and Z, is  .\r\n" );
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document.write( "Thinking this way, we get that the probability for 7 persons to have birthdays in different months is\r\n" );
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document.write( "  ,\r\n" );
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document.write( "which is the product of 6 factors; the structure of the formula is clear.\r\n" );
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document.write( "Making calculations, you get value P = 0.111400463, or 0.11 = 11% rounded.\r\n" );
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document.write( "So, the probability that 7 randomly chosen people have birthdays in different months is 0.11, or 11%.\r\n" );
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document.write( "The probability that of 7 randomly chosen people at least two of them have \r\n" );
document.write( "birthdays in the same month is the complement to 0.11, i.e. 1-0.11 = 0.89.\r\n" );
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document.write( "Thus the probability that John wins is 0.89, or 89%; \r\n" );
document.write( " the probability that Krista wins is 0.11, or 11%.\r\n" );
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document.write( "ANSWER. The probability that Krista wins is 0.11 = 11%.\r\n" );
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document.write( "Solved.\r
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document.write( "If you want to learn more about this subject, read the lesson\r
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document.write( " - Coinciding birthdays \r
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document.write( "in this site.\r
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