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.

i. Show that P(X = 2) = 3/7.

ii. Tabulate the probability distribution of X.

iii. Find E(X ) and Var(X ).

iv. Given that X = 2, find the probability that the digit chosen from set A was 2.