Question

The King, Queen and Jack of clubs are removed from a deck of 52 cards and then well shuffled. One card is selected from the remaining cards. The probability of getting a club is ______.
A. \[{}^{13}/{}_{49}\]
B. \[{}^{10}/{}_{49}\]
C. \[{}^{3}/{}_{49}\]
D. \[{}^{1}/{}_{49}\]

Answer 1

- Hint:- Find the total number of cards in the deck after removing the king, queen and jack of clubs. Thus find the total number of cards in deck after the removal. Probability will be the number of favorable outcomes by the total number of cards.



Complete step-by-step answer: -

There are a total of 52 cards in a deck of playing cards. Out of which, there are 26 back cards and 26 red cards. Out of the red cards there are 13 cards of heart and 13 cards of diamond. And out of the black cards there are 13 cards of spades and 13 cards of clubs. Thus all together they make 52 cards.
The king, queen and jack are called the face cards and there are a total of 12 face cards. It is said that the king, queen and jack of clubs are removed, i.e. out of 12 face cards, 3 face cards are removed.
Now the total deck of cards consists of 40other cards + 12 face cards.
As 3 face cards are removed, there are only 9 face cards now.
\[\therefore \]Total number of cards at present = 40 other cards + 9 face cards = 49 cards.
Thus the total number of cards is 49.
We need to find the probability of getting a club.
We know that there are 13 cards of the club. After removing king, queen and jack of the clubs, only 10 club cards are left in the deck.
Let E be the event of getting a club.
Thus, number of favorable outcomes to E = 10.
\[\therefore \]Required probability P(E) \[=\dfrac{Number\text{ }of\text{ }favorable\text{ }outcomes}{Total\text{ }number\text{ }of\text{ }outcomes}=\dfrac{10}{49}\]
\[\therefore \]Probability of getting a club \[=\dfrac{10}{49}\]
Option B is the correct answer.

Note:
For other cards of diamonds, hearts and spades, we can find the probability out of 49 cards as,
Probability of getting a heart \[=\dfrac{13}{49}\]
Probability of getting a diamond \[=\dfrac{13}{49}\]
Probability of getting a space \[=\dfrac{13}{49}\]