Separate the two-card stopping cases from the squared third-card scores

Four distinct cards are numbered 1,2,3,4. A player randomly picks a pair without replacement. If their sum is odd, that sum is the score. If the sum is even, the player randomly picks a third card from the remaining cards and scores the square of its number.

(i) Find the probability of score 4.

(ii) Find the probability distribution of score S, and hence its expectation.

(iii) Find the probability of a score below 5, given three cards are drawn.