What is the probability of picking a face card given that the card is a king?

Important Notes

• 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

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

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

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 

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.

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.

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.

37.

P(if the series lasts 7 games, Atlanta will win).

We seek P(Atlanta wins | series last 7 games). This is a conditional probability statement and we apply the conditional formula here.

P(Atlanta wins | series last 7 games) = P(Atlanta wins AND series last 7 games)/P(series lasts 7 games)

There are 40 different win-lose sequences that lead to a 7-game series. In 20 of these sequences, Atlanta wins 4 games to 3 and in the other 20, the Yankees win 4 games to 3.

Each of the 20 ways that Atlanta wins the series in 7 games has the same probability: (0.4)^4(0.6)^3 = 0.0055296. So P(Atlanta wins AND series last 7 games) = 20*(0.4)^4(0.6)^3 = 20*0.0055296 = 0.110592.

Each of the 20 ways that the Yankees win the series in 7 games has the same probability: (0.6)^4(0.4)^3 = 0.0082944. So P(Yankees win AND series last 7 games) = 20*(0.6)^4(0.4)^3 = 20*0.0082944 = 0.165888.

Because the event "Yankees win in 7" and the event "Braves win in 7" are mutually exclusive, we add the two results to determine P(series last 7 games). This is 0.165888 + 0.110592 = 0.27648 = P(series last 7 games). This says, by the way, that under these conditions and assumptions, about 25% of the time the series will last 7 games.

We can now compute the desired conditional probability:

P(Atlanta wins | series last 7 games) = P(Atlanta wins AND series last 7 games)/P(series lasts 7 games) = (0.110592)/(0.165888 + 0.110592) = 0.4. Does this seem like a surprising result? Given that we get to game 7, we can think of the series boiling down to one game, and the probability that atlanta wins that one game is just P(B) = 0.4.

Another way to think about (0.110592)/(0.165888 + 0.110592) is top think of it as a weighted outcome: P(result A and condition #1) compared to the sum of the probabilities of all possible results under condition #1. Here, there were just two results possible under the condition that we get to game 7: Either the Braves win or the Yankees win.

Other situations may extend that. Suppose under a certain condition, 10 different things - - all mutually exclusive - - could happen. Then the probability that the first of those different things does happen under the given condition is just the probability that that first thing happens and the condition happens compared to the sum of the 10 probabilities for the 10 different things that could happen with the condition in place.