What is the theoretical probability of of drawing a non-face card from a 52 card standard Hoyle deck?

a card is randomly selected from a deck of card. Find the probability that it is a black card or a face card

6 years ago

There are 52 cards in a deck in total. Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades). There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total). Diamonds and Hearts are red cards (there are 26 total red cards) and Clubs and Spades are black cards (there are 26 total black cards).

There are 26 black cards and 12 face cards in total. However, of those 26 black cards, there are 6 face cards. That means there are 26+12-6 = 32 cards in total that are either a black card or a face card, but not both. That means the answer to the question is 32/52 = 8/13.

Take this 5-min test to see how close you are to achieving your language learning goals.

6 years ago

A = number of black cards B = number of picture cards (or face cards) C = number of black picture cards

There are 26 black cards (spades and clubs), so A = 26.

There are 3 picture cards (Jack, Queen, King) in each suit. There are 4 suits (clubs, hearts, spades, diamonds). So there are 3*4 = 12 picture cards. This means B = 12

There are 2 suits which are black (spades and clubs) with 3 face cards per suit, so 2*3 = 6 cards which are both black cards and face cards. So C = 6

The number of cards that are either black cards or a face card, or both, is...

D = A+B-C D = 26+12-6

D = 32

So there are 32 cards that are either black cards or a face card, or both

This is out of 52 cards total, so

probability of selecting a black card or a picture card = D/52

probability of selecting a black card or a picture card = 32/52

probability of selecting a black card or a picture card = 8/13

The final answer, as a fraction, is 8/13

Find an online tutor for 1-on-1 lessons and master the knowledge you need! Prices from just $5 per hour.

Preply uses cookies according to the settings of your browser. Detailed information can be found in the Cookies Policy

In this post I’ll answer the question, How many non-face cards are in a deck of 52 cards?  As well as some other related questions about non-face cards in a standard deck of cards.

Table of Contents

What are Non-Face Cards?

The non-face cards are all the cards that are not specifically face cards in a deck.  Since the face cards are the Jacks, Queens, and Kings (think of them as all the cards with faces on them), the non-face cards are all the cards except for the Jacks, Queens, and Kings in a deck.

FREE Card Magic eBook & Tricks!I'll send you a FREE card magic book where you can learn some of the greatest secrets of card magic and some great tricks! Plus, I'll keep you updated with FREE magic tricks and tips!

>Click Here!<

This ends up being all the number cards, including the Ace, which represents the number 1 in a deck.  These number cards are the Ace through 10, and in order are the:

• Aces
• Twos
• Threes
• Fours
• Fives
• Sixes
• Sevens
• Eights
• Nines
• Tens

There are 40 non-face cards in a deck of 52 cards.  This is because there are four suits in a deck, (the Spades, Clubs, Hearts and Diamonds), and each of these suits gets one of each of the number cards, or non-face cards.  There are 10 number cards, Ace through ten, and since each of the 4 suits gets 1 of each of these 10 cards, then 4 x 10 gives a total of 40 cards.

See also  How Many Cards are in a Deck with Jokers?

You can also look at it from the fact that there are 12 face cards in a deck.  So that means 52-12=40.  So out of 52 total cards, if 12 of them are face cards, that leaves 40 cards that are not face cards, or non-face cards.

What is a Non-Face Card Called?

Non-face cards are usually called spot cards.  This is because on the card, its value is represented by the same number of spots, or “pips” in the center of the card.

So, for example, a Two of Clubs, has two small pictures of clubs (pips) in the center of the card.  The Three of Hearts has three pips (small hearts) in the center of its card.  And so on for all the number cards.

The probability of getting a non-face card from a deck of 52 cards, would be 40/52, or 10/13.

This is because there are 40 non-face cards that can be possibly chosen, out of a total of 52 cards.

Learn more about why this is at Deck of Cards Probability Explained.

Here are all the non-face cards in a deck of 52 cards.

1. Ace of Hearts
2. Two of Hearts
3. Three of Hearts
4. Four of Hearts
5. Five of Hearts
6. Six of Hearts
7. Seven of Hearts
8. Eight of Hearts
9. Nine of Hearts
10. Ten of Hearts
11. Ace of Diamonds
12. Two of Diamonds
13. Three of Diamonds
14. Four of Diamonds
15. Five of Diamonds
16. Six of Diamonds
17. Seven of Diamonds
18. Eight of Diamonds
19. Nine of Diamonds
20. Ten of Diamonds
21. Ace of Spades
22. Two of Spades
23. Three of Spades
24. Four of Spades
25. Five of Spades
26. Six of Spades
27. Seven of Spades
28. Eight of Spades
29. Nine of Spades
30. Ten of SpadesAdvertisements
31. Ace of Clubs
32. Two of Clubs
33. Three of Clubs
34. Four of Clubs
35. Five of Clubs
36. Six of Clubs
37. Seven of Clubs
38. Eight of Clubs
39. Nine of Clubs
40. Ten of Clubs

See also  Types of Cards in a Deck of 52 Cards

Final Thoughts

We’ve learned that there are a total of 40 non-face cards in a deck.  These are cards are all the number cards from Ace through Ten in each of the four suits.  These non-face cards are also called spot cards.  And the probability of drawing a non-face card from a deck of cards would be 10/13.