6 Pack \(A\) consists of ten cards numbered \(0,0,1,1,1,1,1,3,3,3\). Pack \(B\) consists of six cards numbered \(0,0,2,2,2,2\). One card is chosen at random from each pack. The random variable \(X\) is defined as the sum of the two numbers on the cards.

1. Show that \(\mathrm { P } ( X = 2 ) = \frac { 2 } { 15 }\).
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2. Draw up the probability distribution table for \(X\).
3. Given that \(X = 3\), find the probability that the card chosen from pack \(A\) is a 1 .