From a pack of 52 playing cards Jacks, queens, Kings and aces of red colour are removed.

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 red card

(iii) a black jack

(iv) a picture card (Jacks, queens and Kings are picture cards).

Solution:

Given: The Kings, Queens, Aces and Jacks of red color are removed from a deck of 52 playing cards and the remaining cards are shuffled and a card is drawn at random from the remaining cards

TO FIND: Probability of getting a card of

(i) A black queen

(ii) A red card

(iii) A black jack

(iv) A picture card

After removing the kings, queens, aces and the jacks of red color from the pack of 52 playing cards

Total number of cards left: 

(i) Cards which are black queen is 2

We know that PROBABILITY = 

Hence probability of getting a black queen = 

(ii) Cards which are red are from 2 suits

Total number of red cards is 

From this the kings, queens, aces and jacks of red color are taken out.

Hence total number of red cards left is 

We know that PROBABILITY = 

Hence probability of getting a red card is 

(iii) Cards which are black jack are from 2 suits

Total number of black jack is 

We know that PROBABILITY = 

Hence probability of getting a black jack card 

(iv) Cards which are picture cared are from 4 suits

Total number of picture cards is 

From this the kings, queens, and jacks of red color are taken out.

Hence total number of picture card left is 

We know that PROBABILITY = 

Hence probability of getting an picture card = 

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