Question

The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card of spade.

Answer 1

Hint: We will first calculate the number of remaining cards after removal of King, Queen and Jack of clubs from the deck. If the card is selected from the remaining cards then the number of total cards will be 49 as 3 cards have been removed. We need to find the probability of getting a card of spade, so, we will calculate the total possible outcomes and then we will find the probability of getting a card of spade using the formula:
Probability = (total number of possible outcomes) / (total number of outcomes)

Complete step-by-step answer:
We are given that from a pack of 52 cards, 3 cards, King, Queen, Jack of clubs, are removed.
Therefore, the total number of remaining cards = 52 – 3 = 49
Therefore, the total number of outcomes will also be 49.
A card is then selected from the remaining pack.
We need to find the probability of getting a card of spade.
There are a total 13 cards of each club, spade, diamond and hearts. So, the total number of possible outcomes of getting a card of spade will be 13.
By the definition of probability,
Probability = (total number of possible outcomes) / (total number of outcomes)
$ \Rightarrow $probability = $\dfrac{{13}}{{49}}$
Hence, the probability of getting a card of spade is $\dfrac{{13}}{{49}}$.

Note: In this question, you should be careful while calculating the total number of the possible outcomes and also while calculating the total number of outcomes. You can also solve this question by using the conditional probability.