For X:-
Probability that the card drawn is a black card
=Probability that the card drawn is a king
=Probability that the card drawn is a black king
=Therefore probability The card drawn is black or a king.
=+−=For Y:-
Probability that the card drawn is a club card
=Probability that the card drawn is a heart card
=Probability that the card drawn is a jack
=Probability that the card drawn is a jack of club or a jack of heart
=Therefore probability The card drawn is a club or a heart or a jack
=++−=For Z:-
Probability that the card drawn is a diamond card
=Probability that the card drawn is an ace card
=Probability that the card drawn is a queen card
=Probability that the card drawn is a diamond card of ace or queen
=Therefore the probability The card drawn is an ace or a diamond or a queen.
=++−=Therefore, P(X) = P(Y ) > P(Z)
Therefore option C is the correct answer.