In: Statistics and Probability
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.
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