document.write( "Question 1160944: Suppose that, when a child is born, the probability it’s a girl is a half, and that the sex of the child does not depend on that of another sibling. Find the probability distribution of a number in a family of 4 children and estimate its standard deviation. \n" ); document.write( "
Algebra.Com's Answer #784742 by solver91311(24713)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "Let represent the number of girls children in a family with four children. (This is mathematics, so I don't care about a child's gender identification. I'm only counting children with two X chromosomes as girls)\r
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\n" ); document.write( "\n" ); document.write( "There is exactly one way for all four children to be girls. In a family with three girls and one boy, there are four possibilities, i.e, the boy could be born either first, second, third, or fourth. In a family with two girls and two boys, the possibilities are GGBB, GBGB, GBBG, BGGB, BGBG, BBGG -- a total of six ways. Similarly to three girls and one boy, three boys and one girl have four possible arrangements, and there is only one possibility for four boys.\r
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\n" ); document.write( "\n" ); document.write( "All together there are 16 possibilities: 1 + 4 + 6 + 4 + 1.\r
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\n" ); document.write( "\n" ); document.write( "The probabilities are summarized in the following table:\r
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document.write( "  x    P(x)   xP(x)   (x - μ)²P(x)\r\n" );
document.write( "  4    1/16    1/4	   1/4\r\n" );
document.write( "  3    4/16    3/4         1/4\r\n" );
document.write( "  2    6/16    3/4          0\r\n" );
document.write( "  1    4/16    1/4         1/4\r\n" );
document.write( "  0    1/16     0          1/4\r\n" );
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document.write( "    μ = ΣxP(x)    σ² = Σ[(x - μ)²P(x)] 	  				\r\n" );
document.write( "    μ = 2	  σ² = 1\r\n" );
document.write( "                  σ  = √(1) = 1\r\n" );
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\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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