Question

The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs (iv) a face card (v) a queen of diamond.

Answer 1

Given: King, Queen and Jack of Clubs 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

(i) Heart

(ii) Queen

(iii) Clubs

After removing the king, queen and the jack of clubs from the pack of 52 playing cards

Total number of cards left:

(i) Cards which are heart

Total number of heart cards is

We know that PROBABILITY =

Hence probability of getting a heart card is equal to

(ii) Cards which are queen

Total number of queen cards is

From this 4 queen cards one queen of club is taken out.

Hence total number of queen cards left is

We know that PROBABILITY =

Hence probability of getting an queen card

(iii) Cards which are clubs

Total number of club cards is

The king, queen and jack of clubs are removed

Hence total number of club cards left is

We know that PROBABILITY =

Hence probability of getting a club card is equal to

(iv) a face card
Total face cards = 3 × 4 = 12
king, queen and jack of clubs are removed from the pack
So, face cards left = 12 − 3 = 9
Total cards left = 52 − 3 = 49
Probability of getting a face card = =$=\frac{9}{49}$

(v) a queen of diamond
After removing king, queen and jack of clubs we are left with 52 − 3 = 49 cards total
Probability of getting queen of diamond = $\frac{1}{49}$