52 Card Deck
Playing cards probability problems based on a well-shuffled deck of 52 cards.
Just a shuffled deck of cards; a standard 52 pack. Easy to use, and full screen. Perfect if you are playing Kings, or Hi-Low. You may have found this site by searching for random card generator, deck of cards, random number, virtual playing cards, online cards, internet cards, mobile cards, full screen deck, card dealing, randomizer, coin flip, or dice. There are a total of 52 cards in a deck, each is a week, 52 weeks in a year. The four suits represents the four seasons: Spring, Summer, Fall and Winter. Each suit has thirteen cards, there are.
There are 52 cards in a standard playing card deck, plus a Joker, so if you don't have a tarot deck, you'll be playing without the knights and most of the Major Arcana. What is the Major Arcana? The Major Arcana, also known as the trump cards, are 22 picture cards that have archetypal and allegorical meanings and divine Egyptian, kabbalistic. Card decks and magic tricks. I farkin love this place can I say that lol just recently discovered 52 kards during lockdown and so my deck collection begins can't nthink of a better way to spend time working on card magic and cardistry oh and got a cool 52kards sticker to pimp out my steamer trunks.
Basic concept on drawing a card:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣.
Cards of Spades and clubs are black cards.
Cards of hearts and diamonds are red cards.
The card in each suit, are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2.
King, Queen and Jack (or Knaves) are face cards. So, there are 12 face cards in the deck of 52 playing cards.
Worked-out problems on Playing cards probability:
1. A card is drawn from a well shuffled pack of 52 cards. Find theprobability of:
(i) ‘2’ of spades
(ii) a jack
(iii) a king of red colour
(iv) a card of diamond
(v) a king or a queen
(vi) a non-face card
(vii) a black face card
(viii) a black card
(ix) a non-ace
(x) non-face card of black colour
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king
Solution:
In a playing card there are 52 cards.
Therefore the total number of possibleoutcomes = 52
(i) ‘2’ of spades:
Number of favourable outcomes i.e. ‘2’ ofspades is 1 out of 52 cards.
Therefore, probability of getting ‘2’ ofspade
Number of favorable outcomesP(A) = Total number of possible outcome
= 1/52
(ii) a jack
Number of favourable outcomes i.e. ‘a jack’is 4 out of 52 cards.
Therefore, probability of getting ‘a jack’
Number of favorable outcomesP(B) = Total number of possible outcome
= 4/52
= 1/13
(iii) a king of red colour
Number of favourable outcomes i.e. ‘a kingof red colour’ is 2 out of 52 cards.
Therefore, probability of getting ‘a kingof red colour’
Number of favorable outcomesP(C) = Total number of possible outcome
= 2/52
= 1/26
(iv) a card of diamond
Number of favourable outcomes i.e. ‘a cardof diamond’ is 13 out of 52 cards.
Therefore, probability of getting ‘a cardof diamond’
Number of favorable outcomesP(D) = Total number of possible outcome
= 13/52
= 1/4
(v) a king or a queen
Total number of king is 4 out of 52 cards.
Total number of queen is 4 out of 52 cards
Number of favourable outcomes i.e. ‘a kingor a queen’ is 4 + 4 = 8 out of 52 cards.
Therefore, probability of getting ‘a kingor a queen’
Number of favorable outcomesP(E) = Total number of possible outcome
= 8/52
= 2/13
(vi) a non-face card
Total number of face card out of 52 cards =3 times 4 = 12
Total number of non-face card out of 52cards = 52 - 12 = 40
Therefore, probability of getting ‘anon-face card’
Number of favorable outcomesP(F) = Total number of possible outcome
= 40/52
= 10/13
(vii) a black face card:
Cardsof Spades and Clubs are black cards.
Number of face card in spades (king, queenand jack or knaves) = 3
Number of face card in clubs (king, queen andjack or knaves) = 3
Therefore, total number of black face cardout of 52 cards = 3 + 3 = 6
Therefore, probability of getting ‘a blackface card’
Number of favorable outcomesP(G) = Total number of possible outcome
= 6/52
= 3/26
(viii) a black card:
Cards of spades and clubs are black cards.
Number of spades = 13
Number of clubs = 13
Therefore, total number of black card outof 52 cards = 13 + 13 = 26
Therefore, probability of getting ‘a blackcard’
Number of favorable outcomesP(H) = Total number of possible outcome
= 26/52
= 1/2
(ix) a non-ace:
Number of ace cards in each of four suits namelyspades, hearts, diamonds and clubs = 1
Therefore, total number of ace cards out of52 cards = 4
Thus, total number of non-ace cards out of52 cards = 52 - 4
= 48
Therefore, probability of getting ‘anon-ace’
Number of favorable outcomesP(I) = Total number of possible outcome
= 48/52
= 12/13
(x) non-face card of black colour:
Cards of spades and clubs are black cards.
Number of spades = 13
Number of clubs = 13
Therefore, total number of black card outof 52 cards = 13 + 13 = 26
Number of face cards in each suits namelyspades and clubs = 3 + 3 = 6
Therefore, total number of non-face card ofblack colour out of 52 cards = 26 - 6 = 20
Therefore, probability of getting ‘non-facecard of black colour’
Number of favorable outcomesP(J) = Total number of possible outcome
= 20/52
= 5/13
(xi) neither a spade nor a jack
Number of spades = 13
Total number of non-spades out of 52 cards= 52 - 13 = 39
Number of jack out of 52 cards = 4
Number of jack in each of three suitsnamely hearts,diamonds and clubs = 3
[Since, 1 jack is already included in the13 spades so, here we will take number of jacks is 3]
Neither a spade nor a jack = 39 - 3 = 36
Therefore, probability of getting ‘neithera spade nor a jack’
Number of favorable outcomesP(K) = Total number of possible outcome
= 36/52
= 9/13
(xii) neither a heart nor a red king
Number of hearts = 13
Total number of non-hearts out of 52 cards= 52 - 13 = 39
Therefore, spades, clubs and diamonds arethe 39 cards.
Cardsof hearts and diamonds are red cards.
Number of red kings in red cards = 2
Therefore, neither a heart nor a red king =39 - 1 = 38
[Since, 1 red king is already included inthe 13 hearts so, here we will take number of red kings is 1]
Therefore, probability of getting ‘neithera heart nor a red king’
Number of favorable outcomesP(L) = Total number of possible outcome
= 38/52
= 19/26
2. A card is drawn at random from a well-shuffled pack of cards numbered 1 to 20. Find the probability of
(i) getting a number less than 7
(ii) getting a number divisible by 3.
Solution:
(i) Total number of possible outcomes = 20 ( since there are cards numbered 1, 2, 3, ..., 20).
Number of favourable outcomes for the event E
= number of cards showing less than 7 = 6 (namely 1, 2, 3, 4, 5, 6).
So, P(E) = (frac{textrm{Number of Favourable Outcomes for the Event E}}{textrm{Total Number of Possible Outcomes}})
= (frac{6}{20})
= (frac{3}{10}).
(ii) Total number of possible outcomes = 20.
Number of favourable outcomes for the event F
= number of cards showing a number divisible by 3 = 6 (namely 3, 6, 9, 12, 15, 18).
So, P(F) = (frac{textrm{Number of Favourable Outcomes for the Event F}}{textrm{Total Number of Possible Outcomes}})
= (frac{6}{20})
= (frac{3}{10}).
3. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is
(i) a king
(ii) neither a queen nor a jack.
Solution:
Total number of possible outcomes = 52 (As there are 52 different cards).
(i) Number of favourable outcomes for the event E = number of kings in the pack = 4.
So, by definition, P(E) = (frac{4}{52})
= (frac{1}{13}).
(ii) Number of favourable outcomes for the event F
= number of cards which are neither a queen nor a jack
52 Card Deck Probability
= 52 - 4 - 4, [Since there are 4 queens and 4 jacks].
= 44
Therefore, by definition, P(F) = (frac{44}{52})
= (frac{11}{13}).
These are the basic problems on probability with playingcards.
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