Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The total number of socks = 6 + 4 + 2 = 12.
Probability that two socks match means 2 red socks or 2 green socks or 2 black socks.
[tex]P(\text{2 socks match})= P(RR) + P(GG) +P(BB) [/tex]
When the first sock is picked, the number of socks of that particular colour reduces by 1 as well as the total number of socks.
[tex]P(RR)=\dfrac{6}{12}\times\dfrac{5}{11}=\dfrac{30}{132}[/tex] (There were initially 6 red. When one is picked, we have 5 red remaining to pick the second sock from)
[tex]P(GG)=\dfrac{4}{12}\times\dfrac{3}{11}=\dfrac{12}{132}[/tex]
[tex]P(BB)=\dfrac{2}{12}\times\dfrac{1}{11}=\dfrac{2}{132}[/tex]
[tex]P(\text{2 socks match})= \dfrac{30}{132} + \dfrac{12}{132} + \dfrac{2}{132}=\dfrac{44}{132}=\dfrac{1}{3}[/tex]
