document.write( "Question 1150805: Please help me solve this question: A family plans to have 3 children. Determine the probability that the family will have exactly 1 boy, given that the second child is a boy . \n" ); document.write( "

Algebra.Com's Answer #772277 by ikleyn(52910) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " The problem can be solved by various ways.\r
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\n" ); document.write( "\n" ); document.write( "Solution 1. Make and use the sample space directly and explicitly.\r
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document.write( "The sample space is \r\n" );
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document.write( "    BBB  BBG  BGB  BGG  GBB  GBG  GGB  GGG\r\n" );
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document.write( "(by coding B = boy,  G = girl).\r\n" );
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document.write( "All outcomes are equally likely with the probability of   =   each.\r\n" );
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document.write( "The number of outcomes with a boy as a second child is 4  (BBB  BBG  GBB  GBG).\r\n" );
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document.write( "Of them,  the number of outcomes with only one boy in the family is 1 (GBG).\r\n" );
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document.write( "Hence, the probability under the question is  P = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2. Logical analysis.\r
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document.write( "If the boy (B) is in the 2-nd  of the 3 positions, then for the 1-st and for 3-rd position only  G  is possible.\r\n" );
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document.write( "Each G at the 1-st position and each G at the 3-rd position goes with the probability of .\r\n" );
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document.write( "Hence, the probability to have  G  at  the 1-st and 3-rd positions, under the condition, that the 2-nd position is B, is   = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "In both solutions, you have the same ANSWER :\r
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document.write( "          the probability under the question is  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered, and explained.\r
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