In a drawer there are 4 white socks, 3 blue socks and 5 grey socks. Two socks are picked randomly. What is the possibility that both the socks are of same color?

Solution(By Examveda Team)

Total socks = 4 + 3 + 5 = 12
We want same color socks
So we want, 2 white or 2 blue or 2 grey socks
For white :
Probability of 1^st sock being white = $$\frac{{4}}{{12}}$$
Probability of 2^nd sock being white = $$\frac{{3}}{{11}}$$
White Probability
$$\eqalign{ & = \frac{4}{{12}} \times \frac{3}{{11}} \cr & = \frac{1}{{11}} \cr} $$
Similarly,
Blue Probability
$$\eqalign{ & = \frac{3}{{12}} \times \frac{2}{{11}} \cr & = \frac{1}{{22}} \cr} $$
Grey Probability
$$\eqalign{ & = \frac{5}{{12}} \times \frac{4}{{11}} \cr & = \frac{5}{{33}} \cr} $$
∴ Total Probability
$$\eqalign{ & = \frac{1}{{11}} + \frac{1}{{22}} + \frac{5}{{33}} \cr & = \frac{{19}}{{66}} \cr} $$