A family has 4 children. Assume that each child is as likely to be a boy as it is to be a girl.

A family has 4 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 4 girls if it is known the family has at least one girl.

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Expert Solution

each child is as likely to be a boy as it is to be a girl

total combination of four children

These are all sixteen possibilities. B stands for boy and G stands for girl

BBBB
BBBG
BBGB
BBGG
BGBB
BGBG
BGGB
BGGG
GBBB
GBBG
GBGB
GBGG
GGBB
GGBG
GGGB
GGGG

P(all boys) = 1/16

P(atleast 1 girl) = 1 - P(all boys) = 1-1/16=15/16

now,P(4 girls | atleast 1 girl) = P(4girls) / P(atleast 1 girl) = (1/16) / (1/15) = 1/15

so, answer is 1/15

orchestra answered 1 year ago

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