The king, queen and jack of clubs are removed from a deck of $52$ playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting a club.

Open in App

Solution

Step 1 Finding the total number of outcomes and the number of favorable outcomes:
The event is the selecting a card from the pack.
There are ten of all four suits(Hearts, Diamonds, Spades, and Clubs) from which king, queen, and jack of clubs are removed.
$T o t a l O u t c o m e = T o t a l c a r d s - (K i n g o f C l u b + Q u e e n o f C l u b + J a c k o f C l u b) T o t a l O u t c o m e = 52 - (1 + 1 + 1) T o t a l O u t c o m e = 52 - 3 T o t a l O u t c o m e = 49$
So, the total number of outcomes is $49$ .
Out of the total number of outcomes, the number of clubs is $13$ , but the king, queen, and jack of clubs have been already removed.
$N u m b e r o f c l u b s = 13 - (K i n g o f C l u b + Q u e e n o f C l u b + J a c k o f C l u b) N u m b e r o f c l u b s = 13 - (1 + 1 + 1) N u m b e r o f c l u b s = 13 - 3 N u m b e r o f c l u b s = 10$
So, the number of favorable outcomes is $10$ .
Step 2 Finding the probability of getting a club:
The formula for probability is,
$\Rightarrow P r o b a b i l i t y = \frac{N u m b e r o f f a v o r a b l e o u t c o m e s}{T o t a l n u m b e r o f o u t c o m e s} ∴ P (a c l u b) = \frac{10}{49}$
Therefore, the probability of getting a club is $\frac{10}{49}$ .

Suggest Corrections

Similar questions

Q. The king, queen and jack of clubs are removed from a deck of

52

playing cards and then well-shuffled. One card is selected from the remaining cards. The probability of getting a club is ___________.

The king, queen and jack of clubs are removed from a deck of $52$ playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting a heart.

Q. The king, queen and jack of clubs are removed from 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
A King.

Q. The king, queen and jack of clubs are removed from 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 queen of diamond.

Join BYJU'S Learning Program

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting a club.

The king, queen and jack of clubs are removed from a deck of $52$ playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting a club.