What is the probability of getting a red card or king from a deck of cards?

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How to Determine the Probability of Drawing a Card?
Solved Examples
Interactive Questions
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2. What is the probability of drawing any face card?
3. What is the probability of drawing a red card?
4. What is the probability of drawing a king or a red card?
5. What is the probability of drawing a king or a queen?
6. What are the 5 rules of probability?
7. What is the probability of drawing a king of hearts?
8. Is Ace a face card in probability?
9. What is the probability it is not a face card?
10. How many black non-face cards are there in a deck?
Terms related to probability
Similar Questions

The sample space for a set of cards is 52 as there are 52 cards in a deck. This makes the denominator for finding the probability of drawing a card as 52.
Learn more about related terminology of probability to solve problems on card probability better.

The suits which are represented by red cards are hearts and diamonds while the suits represented by black cards are spades and clubs.

There are 26 red cards and 26 black cards.

Let's learn about the suits in a deck of cards.

Suits in a deck of cards are the representations of red and black color on the cards.

Based on suits, the types of cards in a deck are:

There are 52 cards in a deck.

Each card can be categorized into 4 suits constituting 13 cards each.

These cards are also known as court cards.

They are Kings, Queens, and Jacks in all 4 suits.

All the cards from 2 to 10 in any suit are called the number cards.

These cards have numbers on them along with each suit being equal to the number on number cards.

There are 4 Aces in every deck, 1 of every suit.

Tips and Tricks

There are 13 cards of each suit, consisting of 1 Ace, 3 face cards, and 9 number cards.
There are 4 Aces, 12 face cards, and 36 number cards in a 52 card deck.
Probability of drawing any card will always lie between 0 and 1.
The number of spades, hearts, diamonds, and clubs is same in every pack of 52 cards.

Now that you know all about facts about a deck of cards, you can draw a card from a deck and find its probability easily.

How to Determine the Probability of Drawing a Card?

Let's learn how to find probability first.

Now you know that probability is the ratio of number of favorable outcomes to the number of total outcomes, let's apply it here.

Examples

Example 1: What is the probability of drawing a king from a deck of cards?

Solution: Here the event E is drawing a king from a deck of cards.

There are 52 cards in a deck of cards.

Hence, total number of outcomes = 52

The number of favorable outcomes = 4 (as there are 4 kings in a deck)

Hence, the probability of this event occuring is

P(E) = 4/52 = 1/13

\(\therefore\) Probability of drawing a king from a deck of cards is 1/13.

Example 2: What is the probability of drawing a black card from a pack of cards?

Solution: Here the event E is drawing a black card from a pack of cards.

The total number of outcomes = 52

The number of favorable outcomes = 26

Hence, the probability of event occuring is

P(E) = 26/52 = 1/2

\(\therefore\) Probability of drawing a black card from a pack of cards is 1/2.

Solved Examples

Jessica has drawn a card from a well-shuffled deck. Help her find the probability of the card either being red or a King.

Solution

Jessica knows here that event E is the card drawn being either red or a King.

The total number of outcomes = 52

There are 26 red cards, and 4 cards which are Kings.

However, 2 of the red cards are Kings.

If we add 26 and 4, we will be counting these two cards twice.

Thus, the correct number of outcomes which are favorable to E is

26 + 4 - 2 = 28

Hence, the probability of event occuring is

P(E) = 28/52 = 7/13

\(\therefore\) Probability of card either being red or a King card is 7/13.

Help Diane determine the probability of the following:

Drawing a Red Queen
Drawing a King of Spades
Drawing a Red Number Card

Solution

Diane knows here the events E1, E2, and E3 are Drawing a Red Queen, Drawing a King of Spades, and Drawing a Red Number Card.

The total number of outcomes in every case = 52

There are 26 red cards, of which 2 are Queens.

Hence, the probability of event E1 occuring is

P(E1) = 2/52 = 1/26

There are 13 cards in each suit, of which 1 is King.

Hence, the probability of event E2 occuring is

P(E2) = 1/52

Drawing a Red Number Card

There are 9 number cards in each suit and there are 2 suits which are red in color.

There are 18 red number cards.

Hence, the probability of event E3 occuring is

P(E3) = 18/52 = 9/26

\(\therefore\) Diane determined that the probabilities are P(E1) = 1/26, P(E2) = 1/52, and P(E3) = 9/26.

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

We hope you enjoyed learning about probability of drawing a card from a pack of 52 cards with the practice questions. Now you will easily be able to solve problems on number of cards in a deck, face cards in a deck, 52 card deck, spades hearts diamonds clubs in pack of cards. Now you can draw a card from a deck and find its probability easily .

The mini-lesson targeted the fascinating concept of card probability. The math journey around card probability starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that is not only relatable and easy to grasp, but will also stay with them forever. Here lies the magic with Cuemath.

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We find the ratio of the favorable outcomes as per the condition of drawing the card to the total number of outcomes, i.e, 52.

2. What is the probability of drawing any face card?

Probability of drawing any face card is 6/26.

3. What is the probability of drawing a red card?

Probability of drawing a red card is 1/2.

4. What is the probability of drawing a king or a red card?

Probability of drawing a king or a red card is 7/13.

5. What is the probability of drawing a king or a queen?

The probability of drawing a king or a queen is 2/13.

6. What are the 5 rules of probability?

The 5 rules of probability are:

For any event E, the probability of occurence of E will always lie between 0 and 1

The sum of probabilities of every possible outcome will always be 1

The sum of probability of occurence of E and probability of E not occuring will always be 1

When any two events are not disjoint, the probability of occurence of A and B is not 0 while when two events are disjoint, the probability of occurence of A and B is 0.

As per this rule, P(A or B) = (P(A) + P(B) - P(A and B)).

7. What is the probability of drawing a king of hearts?

Probability of drawing a king of hearts is 1/52.

8. Is Ace a face card in probability?

No, Ace is not a face card in probability.

9. What is the probability it is not a face card?

The probability it is not a face card is 10/13.

10. How many black non-face cards are there in a deck?

There are 20 black non-face cards in a deck.

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A probability is a number that expresses the chance or likelihood of an event occurring. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%, where 0 indicates an impossible event and 1 indicates a certain event. The sum of the probabilities of all the events in a sample space adds up to 1.

There are numerous applications of probability in real life. It is widely used in weather forecasting, typing on smart devices, flipping a coin or dice, sports, traffic signals, video games, and board games in taking medical decisions.

Formula for computing probability

P(E)=
where,
P(E) is the Probability of an event E,
n(E) is the number of favorable outcomes
n(S) is the total number of outcomes in the sample space

Random Experiment: The action of achieving a set of possible outcomes without any prior conscious decision is called as a Random experiment. The prediction of a certain outcome of a random event is known as probability. Random trials include, for example, tossing a coin, drawing a card from a deck, and rolling a dice.

Outcome: An outcome is the result of any random experiment. Suppose if we roll a dice and we get a five. So, rolling a die is a random experiment that yielded the result “five”.

Sample space: It’s a collection of all plausible outcomes from a random experiment. For example, we can get one of the following numbers while rolling a die: 1, 2, 3, 4, 5, 6. As a result, the sample space consists of 1, 2, 3, 4, 5, and 6. This means that if a die is tossed, there are six sample spaces or probable outcomes.

Event: It is the result of a single experiment. Getting a Heads when tossing a coin is an example of an event.

Types of events:

Complementary events: The likelihood that there will only be two outcomes, one of which states whether or not an event will take place. Complementary occurrences include things like today will either rain or not rain, the student will either pass or fail the exam, getting a job or not getting a job, and so on. In other words, the probability of an event occurring in the exact opposite direction of the probability of it not occurring.
Mutually exclusive events: Mutually exclusive events are those in which the occurrence of one event precludes the occurrence of another, i.e. two events have no common point. For example, if S = 1, 2, 3, 4, 5, 6, and E1, E2 are two events, E1 consists of numbers less than 3 and E2 consists of numbers higher than 4, then E1 consists of numbers less than 3 and E2 consists of numbers greater than 4. As a result, E1 = 1,2 and E2 = 5,6. E1 and E2 are hence mutually exclusive events.
Independent events: Independent events are ones whose occurrence is not contingent on the occurrence of another event. For instance, suppose we flip a coin in the air and obtain the result head, then flip the coin again and get the result Tail. The occurrence of these occurrences is independent of one another in both circumstances.
Impossible and Sure Events: An event is called an impossible event if the probability of occurrence is zero, and a sure event if the probability of occurrence is one. To put it another way, the empty set is an impossible event, whereas the sample space S is a sure event.
Exhaustive Events: When all of the events in a set use the whole sample space, it is said to as exhaustive.
Simple Events: In probability, a simple event is an event that consists of a single point in the sample space. For instance, if S = 20, 98, 67, 14, 37 and E = 67, E is a simple event.
Compound Events: A compound event is defined as an event that comprises of more than one single point in the sample space. In the same example, if S = 20, 98, 67, 14, 37, E1 = 20, 67, E2 = 98, 14, 37, E1 and E2 indicate two compound events.
Event E1 but not E2: It symbolizes the distinction between the two occurrences. All the outcomes that are present in E1 but not in E2 are represented by the event E1 but not E2. As a result, the event E1 but not E2 is represented as E1 – E2.
Events Associated with “AND”: If AND is associated with two events E1 and E2, it signifies that the intersection of elements common to both events has occurred. In probability, AND is represented by the intersection symbol (∩). E1 and E2 are thus represented by the event E1∩ E2.
Events Associated with “OR”: If OR is related to two events E1 and E2, it signifies that either E1 or E2 or both are true. In probability, the union symbol (U) is used to indicate OR. As a result, the event E1 U E2 stands for E1 OR E2.

Equally likely events

Equally likely events occur when two or more events have the same theoretical likelihood of occurring. If all of the outcomes of a sample space have the same probability of occurring, they are said to be equally likely. If we throw a dice, for example, the probability of obtaining 1 is 1/6. Similarly, receiving all of the numbers from 2,3,4,5, and 6 one by one has a probability of 1/6. Some other instances of equally likely outcomes when rolling a die are as follows:

Obtaining 2 and 4 on a die toss
Using a die to obtain an even and an odd number

We know that a well-shuffled deck has 52 cards

Total number of suits = 4

Total number of red suits = 2

Since each suite has 13 cards, therefore, the total number of red cards = 2 × 13 = 26

Therefore probability of getting a red card=

Total number of kings in a deck = 4

If we pick one card at random from the 52 cards, the probability of getting a king=

i.e. Probability of getting a king =

Therefore, probability of getting a red card or a king, P(E) = probability of getting a red card+ probability of getting a king

But out of these four kings, two kings are of the red suite and two are of the black suite. This means the probability of getting a red king has been included twice, and hence it should be subtracted.

Hence, probability of getting a red card or a king, P(E) = probability of getting a red card+ probability of getting a king-probability of getting a red king card=