(i) To find the probability \(x\), we use the total probability that Nikita’s mother likes the present:

\(0.3 \times 0.72 + 0.7 \times x = 0.783\)

Simplifying, we get:

\(0.216 + 0.7x = 0.783\)

\(0.7x = 0.783 - 0.216\)

\(0.7x = 0.567\)

\(x = \frac{0.567}{0.7} = 0.81\)

(ii) To find the probability that the present is a scarf given that Nikita’s mother does not like it, we use conditional probability:

\(P(S \mid NL) = \frac{P(S \cap NL)}{P(NL)}\)

\(P(S \cap NL) = 0.3 \times (1 - 0.72) = 0.3 \times 0.28 = 0.084\)

\(P(NL) = 1 - P(L) = 1 - 0.783 = 0.217\)

\(P(S \mid NL) = \frac{0.084}{0.217} \approx 0.387\)

Thus, the probability that the present is a scarf given that Nikita’s mother does not like it is \(0.387\) or \(\frac{12}{31}\).