Question

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is a face card (King, Jack or Queen). 

Answer 1

No. of total cards = 52 

Cards removed of 4 colours of multiples of 3 

= 3, 6, 9

= 4 × 3

= 12

Remaining cards = 52 – 12 = 40

No. of face cards = 12 cards 

${\displaystyle \Rightarrow }$ Probability P(E) = ${\displaystyle \frac{12}{40}=\frac{3}{10}}$ 

Answer 2

The numbers which are multiples of 3 in 52 playing cards are 3, 6 and 9 i.e., 3 cards of each denomination.

∴ All cards whose numbers are multiples of 3 are = 4 × 3 = 12 cards    ...(Jack, Queen and King of each denomination)

Remaining cards = 52 – 12 = 40

Now, Number of face cards = 12

P(face card) = ${\displaystyle \frac{12}{40}=\frac{3}{10}}$.