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Question

# Out of 800 families with 4 children each, the expected percentage of families having almost 2 girls, is:

A
68.75%
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B
69.25%
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C
62.50%
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D
None of these
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Solution

## The correct option is A 68.75%Given: 800 families having 4 children each.To find: the expected percentage of families having almost 2 girlsSol:Let X be the number of boys in a family, If p is the probability that a child is a boy and if genders are independent between children, the probability that a family ends up having k girls isP(X=x)=nCkpk(1−p)n−kHere, n=4,p=12Now we need to find for almost 2 girls, i.e.,P(X=0)+P(X=1)+P(X=2)⟹4C0(12)0(12)4+4C1(12)1(12)3+4C2(12)2(12)2⟹116+4×116+6×116=1116=0.6875Hence the expected percentage of families having almost 2 girls, is 68.75%

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