Assume that each born child is equally likely | vedclass

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(D) Let $B$ denote a boy and $G$ denote a girl. Each family has two children,so there are $2 	imes 2 = 4$ children in total.Total number of outcomes

Vedclass · Accepted Answer

$\frac{1}{11}$

Vedclass · Answer

(D) Let $B$ denote a boy and $G$ denote a girl. Each family has two children,so there are $2 	imes 2 = 4$ children in total.Total number of outcomes for $4$ children is $2^4 = 16$.Let $E$ be the event that all children are girls. $E = \{GGGG\}$,so $n(E) = 1$.Let $F$ be the event that at least two children are girls.$n(F) = n(	ext{exactly 2 girls}) + n(	ext{exactly 3 girls}) + n(	ext{exactly 4 girls})$$n(F) = ^4C_2 + ^4C_3 + ^4C_4 = 6 + 4 + 1 = 11$.The conditional probability $P(E|F) = \frac{n(E \cap F)}{n(F)}$.Since $E \subset F$,$n(E \cap F) = n(E) = 1$.Therefore,$P(E|F) = \frac{1}{11}$.

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,then the conditional probability that all children are girls given that at least two are girls is

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