Hey, the answer to ur question is........
Total girls=2
Total children=6
Therefore, p(getting 2 girl children)=2/6=1/3
Hope this helps u..........
Let the probability of giving birth to a girl is [tex] p=0.5 [/tex].
The number of girls X in a family with 6 children follows binomial distribution.
The probability mass function of binomial random variable X is
[tex] P(X=x)=C(n,6)p^x(1-p)^{n-x} [/tex].
Here [tex] n=6,p=0.5 [/tex]
[tex] P(X=x)=C(x,6)0.5^x(1-0.5)^{6-x}\\
P(X=x)=C(x,6)0.5^6 [/tex]
The required probability is
[tex] \sum_{x=2}^6P(X=x)=\sum_{x=2}^6C(x,6)0.5^6\\
\sum_{x=2}^6P(X=x)=1-\sum_{x=0}^1C(x,6)0.5^6\\
\sum_{x=2}^6P(X=x)=1-(1+6)0.5^6\\
\sum_{x=2}^6P(X=x)=1-\frac{7}{64} \\
\sum_{x=2}^6P(X=x)=\frac{57}{64} [/tex]
