Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, if conditional probability that all children are girls given that at least two are girls is k, then (1/k) =

Question

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, if conditional probability that all children are girls given that at least two are girls is k, then (1/k) = (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let, A = At least two girls B = All girls P((B/A)) = (P(B ∩ A)/P(A)) = (P(B)/P(A)) = (((1/4))4/1 - 4C0 ((1)2)4 - 4C1((1)2)4 = (1/16 - 1 - 4) = (1/11)

Q. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, if conditional probability that all children are girls given that at least two are girls is $k$ , then $\frac{1}{k} =$

Let, $A =$ At least two girls
$B =$ All girls
$P (\frac{B}{A}) = \frac{P ( B \cap A )}{P ( A )} = \frac{P ( B )}{P ( A )}$
$= \frac{( \frac{1}{4} ) ^{4}}{1 - ^{4} C _{0} ( \frac{1}{2} ) ^{4} - ^{4} C _{1} ( \frac{1}{2} ) ^{4}}$
$= \frac{1}{16 - 1 - 4} = \frac{1}{11}$

Q. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, if conditional probability that all children are girls given that at least two are girls is k, then k1​=

Let, A= At least two girls B= All girls P(AB​)=P(A)P(B∩A)​=P(A)P(B)​ =1−4C0​(21​)4−4C1​(21​)4(41​)4​ =16−1−41​=111​

Q. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, if conditional probability that all children are girls given that at least two are girls is $k$ , then $\frac{1}{k} =$

Let, $A =$ At least two girls
$B =$ All girls
$P (\frac{B}{A}) = \frac{P ( B \cap A )}{P ( A )} = \frac{P ( B )}{P ( A )}$
$= \frac{( \frac{1}{4} ) ^{4}}{1 - ^{4} C _{0} ( \frac{1}{2} ) ^{4} - ^{4} C _{1} ( \frac{1}{2} ) ^{4}}$
$= \frac{1}{16 - 1 - 4} = \frac{1}{11}$