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?

Answer: Option D

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
$$\begin{array}{rl}& =\frac{4}{12}\times \frac{3}{11}\\ & =\frac{1}{11}\end{array}$$
Similarly,
Blue Probability
$$\begin{array}{rl}& =\frac{3}{12}\times \frac{2}{11}\\ & =\frac{1}{22}\end{array}$$
Grey Probability
$$\begin{array}{rl}& =\frac{5}{12}\times \frac{4}{11}\\ & =\frac{5}{33}\end{array}$$
∴ Total Probability
$$\begin{array}{rl}& =\frac{1}{11}+\frac{1}{22}+\frac{5}{33}\\ & =\frac{19}{66}\end{array}$$