Question

Face cards of spades are removed from a 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 \[\frac{7}{52}\].

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

Options

• Both the statements are true.

• Both the statements are false.

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

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

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

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 × 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 = \[\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\]

Thus, the probability of drawing a face card from the remaining 49 cards = \[\frac{9}{49}.\]

So, statement 1 is false.

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