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 king.

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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 king is $1$ in all suits except the club.
$N u m b e r o f k i n g s = K i n g o f H e a r t + K i n g o f D i a m o n d + K i n g o f S p a d e N u m b e r o f k i n g s = 1 + 1 + 1 N u m b e r o f k i n g s = 3$
So, the number of favorable outcomes is $3$ .
Step 2 Finding the probability of getting a king:
The formula for probability is,
$\Rightarrow P r o b a b i l i t y = \frac{N u m b e r o f f a v o r a b l e o u t c o m e s}{T o t a l n u m b e r o f o u t c o m e s} ∴ P (n u m b e r o f k i n g) = \frac{3}{49}$
Therefore, the probability of getting a king is $\frac{3}{49}$ .

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