document.write( "Question 1157701: A family has 5 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 5 girls if it is known the family has at least one girl. \n" ); document.write( "

Algebra.Com's Answer #780608 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let represent any possible set of 5 children as a 5-letter world, consisting of letters G or B (G for a girl and B for a boy).\r\n" );
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document.write( "In all,  = 32 such words are possible, having 2 opportunity for each of 5 positions.\r\n" );
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document.write( "The condition \"if it is known the family has at least one girl\" means that we will consider the reduced space of all such words,\r\n" );
document.write( "with the word (BBBBB) removed from the consideration.\r\n" );
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document.write( "This reduced space of events consists of 32-1 = 31 element.\r\n" );
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document.write( "The \"favorable\" set of events consists of only one such word  (GGGGG).\r\n" );
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document.write( "Therefore, the probability under the question is  P = .    ANSWER\r\n" );
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