(i) To find the probability that the socks taken are of different colours, we can use the formula:

\(P(\text{different colours}) = P(RB) + P(BR)\)

Where:

• \(P(RB) = \frac{4}{12} \times \frac{8}{11}\)
• \(P(BR) = \frac{8}{12} \times \frac{4}{11}\)

Thus,

\(P(\text{different colours}) = \frac{4}{12} \times \frac{8}{11} + \frac{8}{12} \times \frac{4}{11} = \frac{16}{33}\)

(ii) The probability distribution table for \(X\), the number of red socks taken, is:

(iii) To find \(E(X)\), the expected value of \(X\), we use:

\(E(X) = 0 \times \frac{14}{33} + 1 \times \frac{16}{33} + 2 \times \frac{3}{33}\)

\(E(X) = \frac{16}{33} + \frac{6}{33} = \frac{22}{33} = \frac{2}{3}\)