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Explanation:

X, Y and Z are events such that

X is the event that the card drawn is black or a king.

Y is the event that the card drawn is a club or a heart or a jack.

Z is the event that the card drawn is an ace or a diamond or a queen.

Consider X.

A black card can be drawn in 26 ways. A king can be drawn in 4 ways. A black king can be drawn in 2 ways.

∴ P(X) = 2652 + 452 - 252

∴ P(X) = 2852

Consider Y.

A club can be drawn in 13 ways. A heart can be drawn in 13 ways. A jack can be drawn in 4 ways. A Jack of hearts can be drawn in 1 way and a jack of club can be drawn in 1 way.

∴ P(X) = 1352 + 1352 + 452 - 152 - 152

∴ P(Y) = 2852

Consider Z.

An ace can be drawn in 4 ways. A queen can be drawn in 4 ways and a diamond can be drawn in 13 ways. Queen of Diamonds can be drawn in 1 way and ace of diamonds can be drawn in 1 way.

∴ P(Z) = 452 + 452 + 1352 - 152 - 152

∴ P(Z) = 1952

∴ P(X) = P(Y) > P(Z)

Hence, option (c).

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