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 an even numbered red card? 

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 

An even number red cards = 2, 4, 8, 10 cards

= 2 × 4

= 8 

${\displaystyle \Rightarrow }$ Probability P(E) = ${\displaystyle \frac{8}{40}=\frac{1}{5}}$

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(even numbered red card) = ${\displaystyle \frac{10}{40}=\frac{1}{4}}$.