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

SOLUTION:

Given : King, queen and jack of club are removed from the Deck of 52 playing cards.

So, remaining cards in deck = 52 - 3 = 49

Total number of outcomes = 49

(i) We know , that there are 13 cards of heart.

Let E1 = event of getting a heart

Number of favourable outcomes to E1= 13

Required probability P(E1)= Number of favourable outcomes / total number of outcomes

P(E1) = 13/49

Hence, the Required probability of getting a heart , P(E1) = 13/49

ii) We know , that there are 4 queens in a deck. After remove removing a queen of club we left with  3 queens.  

Let E2 = event of getting a queen  

Number of favourable outcomes to  E2 = 3

Required probability P(E2) = Number of favourable outcomes / total number of outcomes

P(E2) = 3/49

Hence, the Required probability of getting a queen,  P(E2) = 3/49

(iii) We know, that there are 13 cards of club. After removing king ,queen and jack of club only 10 club cards are left in the deck.

Let E3 = event of getting a club card

Number of favourable outcomes to  E3 = 10

Required probability P(E3) = Number of favourable outcomes / total number of outcomes

P(E3) = 10/49

Hence, the Required probability of getting a club card,  P(E3) = 10/49

(iv) Let E4 = Event  of getting a face card

Number of face card in one Deck of cards = 12

[King, queen ,and jack are called face cards. King, queen, ace and the Jack of club  are removed from the pack of 52 playing cards.

Number of picture cards removed of club  = 3

Number of the remaining face  cards = 12 - 3 = 9

Number of outcome favourable to E4 = 9

Probability (E4) = Number of favourable outcomes / Total number of outcomes

P(E4) = 9/49  

Hence, the required probability of getting a face cards , P(E4) = 9/49 .

(v) We know , that there is 1  queen of diamond  in a deck.

Let E5 = Event of getting a queen of diamond

Number of favourable outcomes to  E5 = 1

Required probability P(E5) = Number of favourable outcomes / total number of outcomes

P(E5) = 1/49

Hence, the Required probability of getting a queen of diamond , P(E5) = 1/49

HOPE THIS ANSWER WILL HELP  YOU….

Answer 2

From a deck of 52 cards, king ,queen , jacks of clubs are removed,
So three cards are removed, hence card left is 52 - 3 = 49 cards
1) Probability of getting a heart
As there are 13 hearts in a deck
So the probability = no of hearts/number of cards = 13/49

2) There are three kings left
Hence probability of getting a king = 3/49

3) Three clubs are removed , so number of clubs is 10
So the probability of getting a club = 10/49

4) 10 of heart is only one card
So the probability = 1/49