The question is a bit vague but will try and asnwer it to the best of my ability.
There are 11 socks i.e. 5 blue socks and 6 black socks. 2 socks were taken out without replacement.
So the probabilities are as follows:
\(P(\text{1st sock is blue} = \frac{5}{11})\)
\(P(\text{1st sock is black} = \frac{6}{11})\)
\(P(\text{2nd sock is blue given 1st is blue} = \frac{4}{10})\)
\(P(\text{2nd sock is black given 1st is blue} = \frac{6}{10})\)
\(P(\text{2nd sock is blue given 1st is black} = \frac{5}{10})\)
\(P(\text{2nd sock is black given 1st is black} = \frac{5}{10})\)
To answer the questions as I understand them.
a) What is the probability the second sock is also black given the first one is black?
\[P(\text{2nd sock is black given 1st is black} = \frac{5}{10}\]
b) What is the probability that both socks are black?
\[P(\text{Black and Black})=\frac{6}{11}\cdot \frac{5}{10}=\frac{30}{110}\]