Question

From a pack of 52 playing cards; Jacks, Queens, Kings and Aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is 

i) a black queen, 

ii) a face card, 

iii) a blackjack, 

iv) a red card.

Answer 1

Total number of cards = 52 

Card removed = 2 + 2 +2 + 2 = 8 

∴ Remaining number of cards = 52 – 8 = 44 

i) Number of black queens = 2 

∴ Required probability = \(\frac{2}{44}=\frac{1}{22}\)

ii) Number of face cards left = 2 + 2 + 2 = 6 

∴ Required probability = \(\frac{6}{44}=\frac{3}{22}\)

iii) Number of blackjacks = 2 

∴ Required probability = \(\frac{2}{44}=\frac{1}{22}\)

iv) Number of red cards left = 26 - 8 = 18

∴ Required probability = \(\frac{18}{44}=\frac{9}{22}\)