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priyanshu463590
@priyanshu463590
May 2021
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Can anyone solve Question 11 ??
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Swarnimkumar22
Verified answer
A Family has 2 children . Find the Probability that both are boys, if it is know that
(i) at least one of the children is a boy
(ii) the elder child is boy
According to the question we know that in a family has two children
Now,
let, B = Boy and G = Girl
then
S = {gg}{bb}{gb}{bg}
(i) When 1 children is boy
B' = {bb}{gb}{bg}
so,
P(B) = 3/4
(ii)
when both children are boys
B = {bb}
so,
P(B') = 1/4
Also,
Now,
3 votes
Thanks 19
abhii67
Answer According to the question we know that in a family has two children
Now,
let, B = Boy and G = Girl
then
S = {gg}{bb}{gb}{bg}
(i) When 1 children is boy
B' = {bb}{gb}{bg}
so,
P(B) = 3/4
(ii)
when both children are boys
B = {bb}
so,
P(B') = 1/4
Also,
\begin{lgathered}B \cap \: B' \: = (b, \: b) \\ \\ p(B \cap B') = \frac{1}{4}\end{lgathered}B∩B′=(b,b)p(B∩B′)=41
Now,
\begin{lgathered}p( \frac{B }{\: B'} ) = \frac{p(B \cap \: B')}{p(B')} \\ \\ = \frac{ \frac{1}{4} }{ \frac{3}{4} } = \frac{1}{3} \\ \\ p( \frac{B }{\: B'} ) = \frac{1}{3}\end{lgathered}p(B′B)=p(B′)p(B∩B′)=4341=31p(B′B)=31
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Answers & Comments
Verified answer
A Family has 2 children . Find the Probability that both are boys, if it is know that
(i) at least one of the children is a boy
(ii) the elder child is boy
According to the question we know that in a family has two children
Now,
let, B = Boy and G = Girl
then
S = {gg}{bb}{gb}{bg}
(i) When 1 children is boy
B' = {bb}{gb}{bg}
so,
P(B) = 3/4
(ii)
when both children are boys
B = {bb}
so,
P(B') = 1/4
Also,
Now,
Now,
let, B = Boy and G = Girl
then
S = {gg}{bb}{gb}{bg}
(i) When 1 children is boy
B' = {bb}{gb}{bg}
so,
P(B) = 3/4
(ii)
when both children are boys
B = {bb}
so,
P(B') = 1/4
Also,
\begin{lgathered}B \cap \: B' \: = (b, \: b) \\ \\ p(B \cap B') = \frac{1}{4}\end{lgathered}B∩B′=(b,b)p(B∩B′)=41
Now,
\begin{lgathered}p( \frac{B }{\: B'} ) = \frac{p(B \cap \: B')}{p(B')} \\ \\ = \frac{ \frac{1}{4} }{ \frac{3}{4} } = \frac{1}{3} \\ \\ p( \frac{B }{\: B'} ) = \frac{1}{3}\end{lgathered}p(B′B)=p(B′)p(B∩B′)=4341=31p(B′B)=31