document.write( "Question 1164268: Given a family with three children, find the probability of the event.
\n" ); document.write( "given that the birth order alternates between girls and boys. What is the probability that the youngest is a boy, given that the birth order alternates between girls and boys? \n" ); document.write( "

Algebra.Com's Answer #788582 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "There are 2*2*2 = 8 possible boy/girl sequences.

\n" ); document.write( "Of those 8, only two are sequences in which the birth order alternates between boys and girls: BGB and GBG.

\n" ); document.write( "Of those two, only one has a boy as the youngest.

\n" ); document.write( "ANSWER: The probability that the youngest is a boy, given that the birth order alternates between boys and girls, is 1/2.

\n" ); document.write( "More formally, using the definition of conditional probability, theprobability that the youngest is a boy, given that the birth order alternates between boys and girls, is:


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document.write( " P((birth order alternates between boys and girls)AND(youngest is a boy))    (1/8) =  1
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document.write( "           P(birth order alternates between boys and girls)                  (2/8) =  2 \n" );
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