# What is the probability of getting king in the pack of 52 cards?

Last updated date: 22nd Mar 2023

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Answer

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Hint: In this question, we first need to look into the pack of cards. We need to know what different kinds of cards are present and the count of them. So, that we can write the number of favourable outcomes for the given condition and the total number of possible outcomes.

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

Complete step-by-step answer:

Let us look into some basic definitions at first.

TRIAL: Let a random experiment be repeated under identical conditions then the experiment is called a trial.

OUTCOME: A possible result of a random experiment is called its outcome.

SAMPLE SPACE: The set of all possible outcomes of an experiment is called the sample space of the experiment and is denoted by S.

SAMPLE POINT: The outcome of an experiment is called sample point.

EVENT: A subset of the sample space associated with a random experiment is said to occur, if any one of the elementary events associated to it is an outcome.

PROBABILITY: If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A, denoted by P(A), is given by

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

The pack of playing cards which count 52 are divided into:

4 suits named spade, heart, club, diamond.

Again, we have 13 cards in each suit.

Out of 13 cards in each suit contain 1 King, 1 Queen, 1 Jack, 1 Ace and 2-10 cards.

Here, King, Queen, Jack are called face cards.

Now, we have 1 King in each suit. As there are 4 suits in total so we have 4 Kings in 52 cards.

Let us assume that drawing a King from a pack of 52 cards as event A.

Number of favourable outcomes = 4

Total number of possible outcomes = 52

\[\begin{align}

& m=4,n=52 \\

& \Rightarrow P\left( A \right)=\dfrac{m}{n} \\

& \therefore P\left( A \right)=\dfrac{4}{52} \\

\end{align}\]

Note: It is important to know about the different types of cards and their count while attempting the problem because neglecting any one of the cards changes the result completely.

Playing cards contain all the other face cards and Ace cards along with the number cards. So, the total count of cards is 52 not 36.

For example, the probability of getting face cards is:

\[\begin{align}

& m=12,n=52 \\

& \Rightarrow P\left( A \right)=\dfrac{m}{n} \\

& \Rightarrow P\left( A \right)=\dfrac{12}{52} \\

& \therefore P\left( A \right)=\dfrac{3}{13} \\

\end{align}\]

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

Complete step-by-step answer:

Let us look into some basic definitions at first.

TRIAL: Let a random experiment be repeated under identical conditions then the experiment is called a trial.

OUTCOME: A possible result of a random experiment is called its outcome.

SAMPLE SPACE: The set of all possible outcomes of an experiment is called the sample space of the experiment and is denoted by S.

SAMPLE POINT: The outcome of an experiment is called sample point.

EVENT: A subset of the sample space associated with a random experiment is said to occur, if any one of the elementary events associated to it is an outcome.

PROBABILITY: If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A, denoted by P(A), is given by

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

The pack of playing cards which count 52 are divided into:

4 suits named spade, heart, club, diamond.

Again, we have 13 cards in each suit.

Out of 13 cards in each suit contain 1 King, 1 Queen, 1 Jack, 1 Ace and 2-10 cards.

Here, King, Queen, Jack are called face cards.

Now, we have 1 King in each suit. As there are 4 suits in total so we have 4 Kings in 52 cards.

Let us assume that drawing a King from a pack of 52 cards as event A.

Number of favourable outcomes = 4

Total number of possible outcomes = 52

\[\begin{align}

& m=4,n=52 \\

& \Rightarrow P\left( A \right)=\dfrac{m}{n} \\

& \therefore P\left( A \right)=\dfrac{4}{52} \\

\end{align}\]

Note: It is important to know about the different types of cards and their count while attempting the problem because neglecting any one of the cards changes the result completely.

Playing cards contain all the other face cards and Ace cards along with the number cards. So, the total count of cards is 52 not 36.

For example, the probability of getting face cards is:

\[\begin{align}

& m=12,n=52 \\

& \Rightarrow P\left( A \right)=\dfrac{m}{n} \\

& \Rightarrow P\left( A \right)=\dfrac{12}{52} \\

& \therefore P\left( A \right)=\dfrac{3}{13} \\

\end{align}\]

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