Question

red Queens and Blackjacks are removed from a pack of 52 playing cards a card is drawn at random from the remaining cards after reshuffling them find the proparbility that the drawn card is a king, either heart or queen, either face card or club and a diamond​

Answer 1

Answer:

Step-by-step explanation:

2 red queens and 2 black jacks are removed from a pack of 52 cards.

So, cards remaining are 48.

∴n(S)=48

We need to find probability that 1 card drawn at random is

(1) a king

There are 4 kings in a pack.

Let A be the event of drawing a king.

∴n(A)=4

Therefore probability of drawing a king from 48 remaining cards is

P(A)=  

n(S)

n(A)

​  

 

P(A)=  

48

4

​  

=  

12

1

​  

 

(2) of red colour

After removing 2 red queens, there remain 24 red colour cards in a pack.

Let B be the event of drawing a red colour card from remaining 48 cards.

∴n(B)=24

Therefore probability of drawing a red colour card is

P(B)=  

n(S)

n(B)

​  

 

P(B)=  

48

24

​  

=  

2

1

​  

 

(3) a face card

2 red  queen and 2 black jacks are removed from a pack. Therefore, total face cards remaining are 8.

Let C be the event of drawing a face card.

∴n(C)=8

Therefore probability of drawing a face card is

P(C)=  

n(S)

n(C)

​  

 

P(C)=  

48

8

​  

=  

6

1

​  

 

(4) a queen

There are remaining only 2 queens after removing 2 red queens.

Let D be the event of drawing a queen.

∴n(D)=2

Therefore probability of drawing a queen is

P(D)=  

n(S)

n(D)

​  

 

P(D)=  

48

2

​  

=  

24

1

​