Question

What is the probability of getting a king if a card is drawn from the pack of \[52\] cards?
A) $\dfrac{1}{{53}}$
B) $\dfrac{2}{{53}}$
C) $\dfrac{3}{{53}}$
D) \[\dfrac{4}{{52}}\]

Answer 1

Hint: We will use the basic definition of probability to determine the required probability. We will first determine the elements in the event and the sample space so that we will just have to divide both quantities in order to calculate the probability.

Complete step-by-step answer:
We have given a normal deck of cards and we have to find the probability of choosing a king out of it.
For a normal event $A$ , if the sample space is denoted by $S$ then the probability of even $A$ happening is given by the following formula:
$P\left( A \right) = \dfrac{{n\left( A \right)}}{{n\left( S \right)}}$
Here the event $A$ be the selection of a king from the pack of given cards.
It can be easily seen that the sample space in the given case will be all cards.
Therefore, $n\left( S \right) = 52$ .
Now we just have to determine the cardinality of the event.
We know that the normal deck of cards contains one king of each suit.
That means we have a total of $4$ kings in any normal deck of cards.
We have to select a king from the kings present in the given deck.
This makes the considered event will have the cardinality $4$ .
Therefore,
$n\left( A \right) = 4$
Therefore, the probability of the given event is:
$P\left( A \right) = \dfrac{4}{{52}}$
Hence, the correct option is D.

Note: The given problem is straight forward to solve. We just have to find the cardinality of the event correctly. Note that the probability is always positive and less than or equal to one. We can follow the same pattern to find the probability of getting any special card from a normal deck of cards.