(i) The probability that Tamar wears red socks is calculated by considering both cases: wearing a blue suit and wearing a grey suit.

Probability of wearing red socks with a blue suit: \(0.6 \times 0.2 = 0.12\).

Probability of wearing red socks with a grey suit: \(0.4 \times 0.32 = 0.128\).

Total probability of wearing red socks: \(0.12 + 0.128 = 0.248\).

Expressed as a fraction: \(\frac{31}{125}\).

(ii) We need to find the probability that Tamar is wearing a grey suit given that he is not wearing red socks.

Probability of not wearing red socks with a blue suit: \(0.6 \times 0.8 = 0.48\).

Probability of not wearing red socks with a grey suit: \(0.4 \times 0.68 = 0.272\).

Total probability of not wearing red socks: \(0.48 + 0.272 = 0.752\).

Using Bayes' theorem, the probability of wearing a grey suit given not wearing red socks is:

\(\frac{0.272}{0.752} = \frac{17}{47}\).