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Considering that each child is equally likely to be a boy or a girl , no of ways of getting 2 girls and 2 boys can be GGBB,GBGB,BBGG,BGBG etc in which there are 4 children out of which 2 are boys and 2 are girls , which equals 4!/2!*2!
Total no of ways is 2n =24 =16.

Hence Probability of a 2:2 boy-girl split : 6/16 = 3/8.

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