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Mathematics

Face cards of spades are remove from the pack of 52 cards and the remaining cards are well shuffled. Then a card is drawn from the pack.

Statement (1): The probability of drawing a face card is 752\dfrac{7}{52}.

Statement (2): Kings, queens and jacks are the three face card and so the total number of face cards in the pack of 52 card is 3 x 4 = 12.

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Probability

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Answer

In a standard deck of 52 playing cards, each suit (hearts, diamonds, clubs, spades) contains 3 face cards: Jack, Queen, and King. Therefore, the total number of face cards in the deck is:

3 x 4 = 12

So, statement 2 is true.

After removing the face cards of spades (Jack, Queen, King), we are left with = 12 - 3 = 9 face cards.

The total number of remaining cards in the deck = 52 - 3 = 49.

By formula; the probability of an event = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

Thus, the probability of drawing a face card from the remaining 49 cards = 949\dfrac{9}{49}.

So, statement 1 is false.

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is the correct option.

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