document.write( "Question 1174578: A family has five children. Assuming that the probability of a girl on each birth was 0.5 and
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Algebra.Com's Answer #800002 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A family has five children. Assuming that the probability of a girl on each birth was 0.5
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document.write( "As it is well known fact, in all, there are   = 32 possible configurations / elements \r\n" );
document.write( "in the space of events, each case with the probability of  .\r\n" );
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document.write( "Since the condition is imposed \"there is at least one boy\", we exclude this singular case\r\n" );
document.write( "of having all 5 girls in the family.\r\n" );
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document.write( "So, the reduced space of events consists now of 32-1 = 31 configurations, with \"all 5 girls\" excluded.\r\n" );
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document.write( "Therefore, the number 31 is the reduced cardinality of the total space of events:  \"total reduced\" = 31.\r\n" );
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document.write( "The problem asks about configurations, in which there is at least one girl - so the case \"all 5 boys\" is excluded.\r\n" );
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document.write( "It reduces the number of \"favorable\" cases from 31 to 31-1 = 30.\r\n" );
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document.write( "THEREFORE, the probability under the problem's question is  P = .    ANSWER\r\n" );
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document.write( "ANSWER.  The probability is  .\r\n" );
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