A card is drawn at random from a well shuffled pack of 52 cards.
X: The card drawn is black or a king.
Y: The card drawn is a club or a heart or a jack.
Z: The card drawn is an ace or a diamond or a queen.
Then which of the following is correct?

For X:-

Probability that the card drawn is a black card = $$\frac{26}{52}$$

Probability that the card drawn is a king = $$\frac{4}{52}$$

Probability that the card drawn is a black king = $$\frac{2}{52}$$

Therefore probability The card drawn is black or a king. = $$\frac{26}{52}$$ + $$\frac{4}{52}$$ - $$\frac{2}{52}$$ = $$\frac{28}{52}$$

For Y:-

Probability that the card drawn is a club card  = $$\frac{13}{52}$$

Probability that the card drawn is a heart card = $$\frac{13}{52}$$

Probability that the card drawn is a jack = $$\frac{4}{52}$$ 

Probability that the card drawn is a jack of club or a jack of heart = $$\frac{2}{52}$$

Therefore probability The card drawn is a club or a heart or a jack  = $$\frac{13}{52}$$ + $$\frac{13}{52}$$ + $$\frac{4}{52}$$ - $$\frac{2}{52}$$ = $$\frac{28}{52}$$

For Z:- 

Probability that the card drawn is a diamond card  = $$\frac{13}{52}$$

Probability that the card drawn is an ace card = $$\frac{4}{52}$$ 

Probability that the card drawn is a queen card = $$\frac{4}{52}$$

Probability that the card drawn is a diamond card of ace or queen = $$\frac{2}{52}$$

Therefore the probability The card drawn is an ace or a diamond or a queen. = $$\frac{13}{52}$$ + $$\frac{4}{52}$$ + $$\frac{4}{52}$$ - $$\frac{2}{52}$$ =  $$\frac{19}{52}$$ 

Therefore, $$P(X) = P(Y) > P(Z)$$ 

Therefore option C is the correct answer.