A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is: i. a card of spade or an ace. ii. a black king. iii. neither a jack nor a king. iv. either a king or a queen.

There are 52 cards in total. Hence, total Outcomes = 52

(i) Probability of the card drawn is a card of spade or an Ace:
Total cards of Spade = 13
Total Aces = 4
Number of Aces of Spade = 1
Therefore, Probability of the card drawn is a card of spade or an Ace: 13/52 + 4/52 - 1/52 = 16/52 = 4/13

(ii) Probability of the card drawn is a black king:
Total black kings: 2
Probability of the card drawn is a black king: 2/52 = 1/26

(iii) Probability of the card drawn is neither a jack nor a king
Total jacks = 4
Total Kings = 4
Probability of the card drawn is neither a jack nor a king: 1 - (4 + 4)/52 = 44/52 = 11/13

(iv) Probability of the card drawn is either a king or a queen:
Total Queens = 4
Total Kings = 4
Probability of the card drawn is either a king or a queen: (4 + 4)/52 = 8/52 = 2/13