Indian Institute of Foreign Trade 2009 Solved Paper

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.