5 Set \(A\) consists of the ten digits \(0,0,0,0,0,0,2,2,2,4\).
Set \(B\) consists of the seven digits \(0,0,0,0,2,2,2\).
One digit is chosen at random from each set. The random variable \(X\) is defined as the sum of these two digits.

1. Show that \(\mathrm { P } ( X = 2 ) = \frac { 3 } { 7 }\).
2. Tabulate the probability distribution of \(X\).
3. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
4. Given that \(X = 2\), find the probability that the digit chosen from set \(A\) was 2 .