1. 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?
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By: anil on 05 May 2019 02.40 am
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.
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