Question

a card is chosen from a well shuffled deck of cards randomly find the probality of the following events

Answer 1

1. The king, queen and jack of clubs are removed from a deck of 52 playing cards and then shuffled. A card is drawn from the remaining cards. Find the probability of getting:

(i) a heart

(ii) a queen

(iii) a club

(iv) ‘9’ of red color


Solution:

Total number of card in a deck = 52

Card removed king, queen and jack of clubs

Therefore, remaining cards = 52 - 3=49

Therefore, number of favorable outcomes = 49

(i) a heart

Number of hearts in a deck of 52 cards= 13

Therefore, the probability of getting ‘a heart’

               Number of favorable outcomes
P(A) =     Total number of possible outcome 

      = 13/49

(ii) a queen

Number of queen = 3

[Since club’s queen is already removed]

Therefore, the probability of getting ‘a queen t’

               Number of favorable outcomes
P(B) =     Total number of possible outcome 

      = 3/49

(iii) a club

Number of clubs in a deck in a deck of 52 cards = 13

According to the question, the king, queen and jack of clubs are removed from a deck of 52 playing cards In this case, total number of clubs = 13 - 3 = 10

Therefore, the probability of getting ‘a club’

               Number of favorable outcomes
P(C) =     Total number of possible outcome 

      = 10/49

(iv) ‘9’ of red color

Cards of hearts and diamonds are red cards

The card 9 in each suit, hearts and diamonds = 1

Therefore, total number of ‘9’ of red color = 2

Therefore, the probability of getting ‘9’ of red color

               Number of favorable outcomes
P(D) =     Total number of possible outcome 

      = 2/49