Card Probability

• 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. 

What Are the Types of Cards in a Deck?

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.

Example 1

 

 

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.

Example 2

 

 

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

• Drawing a Red Queen

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

Hence, the probability of event E₁ occuring is

P(E₁) = 2/52 = 1/26

• Drawing a King of Spades

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.

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Here are a few activities for you to practice.

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

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Let's Summarize

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.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. Be it problems, online classes, videos, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

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