Question

Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is a face card  

Answer 1

In a pack of 52 playing cards, there are 2 red queens and 2 black jacks. 
Red queens and black jacks are removed from the pack. Then,
Number of remaining cards = 52 − 4 = 48
∴ Total number of outcomes = 48 

There are 12 face cards in the pack, out of which 2 red queens and 2 black jacks are removed.
Number of face cards in the remaining pack of cards = 12 − (2 + 2) = 8
So, the favourable number of outcomes are 8.
∴ P(drawing a face card) =

\[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{8}{48} = \frac{1}{6}\]