A family consists of two children. What is the probability that they both are girls?

# A family consists of two children. What is the probability that they both are girls?

1. A
$\frac{1}{4}$
2. B
$\frac{7}{4}$
3. C
$\frac{3}{4}$
4. D
$\frac{5}{4}$

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### Solution:

Given that a family consists of two children.
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
Let girl be 'g' and boy be 'b'. Then,
$S=\left\{\left(g,g\right),\left(g,b\right),\left(b,g\right),\left(b,b\right)\right\}$
$⇒n\left(S\right)=4$
Let E be the event of having both of them as girls.
E = (g, g)
$⇒n\left(E\right)=1$
So the required probability is,
$P\left(E\right)=\frac{\mathit{Outcomes having both girls n}\left(E\right)}{\mathit{Total number of outcomes n}\left(S\right)}$
$⇒P\left(E\right)=\frac{1}{4}$
Thus, the probability of both of them are girl is $\frac{1}{4}$.
Hence, option 1 is correct.

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