(i) To find \(P(X = 2)\), we need the combinations where the sum of the numbers from pack A and pack B equals 2. The possible combinations are:

• Card from A is 0 and card from B is 2: Probability = \(\frac{2}{10} \times \frac{4}{6} = \frac{8}{60} = \frac{2}{15}\)

Thus, \(P(X = 2) = \frac{2}{15}\).

(ii) The probability distribution table for \(X\) is constructed by considering all possible sums:

(iii) Given \(X = 3\), we find the probability that the card from pack A is 1. The combinations for \(X = 3\) are:

• Card from A is 1 and card from B is 2: Probability = \(\frac{5}{10} \times \frac{4}{6} = \frac{20}{60} = \frac{1}{3}\)
• Card from A is 3 and card from B is 0: Probability = \(\frac{4}{10} \times \frac{2}{6} = \frac{8}{60} = \frac{2}{15}\)

Total probability for \(X = 3\) is \(\frac{13}{30}\). The probability that the card from A is 1 given \(X = 3\) is:

\(P(A1 | \text{Sum 3}) = \frac{\frac{5}{10} \times \frac{4}{6}}{\frac{13}{30}} = \frac{10}{13}\)