Question

Pratik has $8$ grey socks and $8$ white socks.

He pulls out two socks randomly without looking at them.

What is the probability of both socks are white?

Answer 1

Find the probability both the socks are white:

Given that Grey socks $=8$, White socks $=8$

$\Rightarrow$Total number of socks$=16$

Probability of an event $E$ is defined by $P\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)}$ where $n\left(E\right),n\left(s\right)$ are the number of favorable outcomes and the total number of possible outcomes respectively.

The probability of pulling the first sock is white$P\left(E_1\right)=\frac{8}{16}=\frac{1}{2}$

Now, Grey socks $=8$, White socks $=7$

Total number of socks remains$=15$

The probability of pulling the white sock is$P\left(E_2\right)=\frac{7}{15}$

The probability of pulling two white socks $P\left(E\right)=P\left(E_1\right)\times P\left(E_2\right)$

$=\frac{1}{2}\times \frac{7}{15}$

$=\frac{7}{30}$

Hence, the probability of pulling two white socks is $\frac{7}{30}$