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.
Answer by solver91311(24713)   (Show Source):
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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)
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.
All together there are 16 possibilities: 1 + 4 + 6 + 4 + 1.
The probabilities are summarized in the following table:
x P(x) xP(x) (x - μ)²P(x)
4 1/16 1/4 1/4
3 4/16 3/4 1/4
2 6/16 3/4 0
1 4/16 1/4 1/4
0 1/16 0 1/4
μ = ΣxP(x) σ² = Σ[(x - μ)²P(x)]
μ = 2 σ² = 1
σ = √(1) = 1
John
My calculator said it, I believe it, that settles it
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