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## Standard 52-card deck

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Cards from a standard 52-card deck

The standard 52-card deck of French-suited playing cards is the most common pack of playing cards used today.[a] In English-speaking countries it is the only traditional pack[b] used for playing cards; in many countries of the world, however, it is used alongside other traditional, often older, standard packs with different suit symbols and pack sizes. The most common pattern worldwide and the only pattern commonly available in Britain and America is the English pattern pack. The second most common is the Belgian-Genoese pattern, designed in France, but whose use spread to Spain, Italy, the Ottoman Empire, the Balkans and much of North Africa and the Middle East.[1] In addition to those, there are other major international and regional patterns.

## Composition

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠), with reversible (double-headed) court cards (face cards). Each suit includes an Ace, a King, Queen and Jack, each depicted alongside a symbol of its suit; and numerals or pip cards from the Deuce (Two) to the Ten, with each card depicting that many symbols (pips) of its suit. Anywhere from one to six (most often two or three since the mid-20th century) Jokers, often distinguishable with one being more colourful than the other, are added to commercial decks, as some card games require these extra cards.[2][3]

Example set of 52 playing cards; 13 of each suit: clubs, diamonds, hearts, and spades

Ace

2

3

4

5

6

7

8

9

10

Jack

Queen

King

Clubs

Diamonds

Hearts

Spades

## Design

Dondorf Rhineland pattern

The most popular standard pattern of the French deck is the English pattern[c] (pictured below), sometimes referred to as the International pattern or Anglo-American pattern.[4] The second most common is the Belgian-Genoese pattern, which was designed in France for export and spread to Spain, Italy, the Ottoman Empire, the Balkans and much of North Africa and the Middle East.[1] There are also numerous others such as the Berlin pattern, Nordic pattern, Dondorf Rhineland pattern (pictured right) and the variants of the European pattern.

Modern playing cards carry index labels on opposite corners or in all four corners to facilitate identifying the cards when they overlap and so that they appear identical for players on opposite sides. For the court cards, this comprises the initial letter or letters from the name of that card. In English countries they are lettered A, K, Q and J for Ace, King, Queen and Jack. In other countries the letters may vary. Germany uses A, K, D and B (As, König, Dame and Bube); Russia uses T, K, D and B (Tuz, Korol, Dama and Valet); Sweden uses E, K, D and Kn (Ess, Kung, Dam and Knekt) and France uses 1, R, D, V (1, Roi, Dame, and Valet).

Although French-suited, 52-card packs are the most common playing cards used internationally, there are many countries or regions where the traditional pack size is only 36 (Russia, Bavaria) or 32 (north and central Germany, Austria) or where regional cards with smaller packs are preferred for many games. For example, 40- or 48-card Italian-suited packs are common in Italy; 40- and 48-card Spanish-suited packs on the Iberian peninsula; and 36-card German-suited packs are very common in Bavaria and Austria. In addition, tarot cards are required for games such as French tarot (78 cards), which is widely played in France, and the Tarock family of games (42 or 54 cards) played in countries like Austria and Hungary.

## History

English pattern

The English pattern pack originated in Britain which was importing French playing cards from Rouen and Antwerp by 1480. The earliest cards of the English pattern date to around 1516. But Britain only started manufacturing its own cards towards the end of the 16th century, when card production began in London. These were based on the Rouen pattern, but unlike the traditional French cards, they dropped the names on the court cards. The English pattern evolved, in the process losing “some of its Rouen flavour and elegance and became more and more stylised. The figures took more space in the cards and many details were distorted.”[4]

All early cards of this type were single-headed, but around 1860, the double-headed cards, universally used on modern decks, appeared. Corner indices were added around 1880. During the 19th century, the English pattern spread all over the world and is now used almost everywhere, even in countries where traditional patterns and other suits are popular. In America, the English pattern was copied onto wider cards.[4]

The fanciful design and manufacturer’s logo commonly displayed on the ace of spades began under the reign of James I of England, who passed a law requiring an insignia on that card as proof of payment of a tax on local manufacture of cards. Until August 4, 1960, decks of playing cards printed and sold in the United Kingdom were liable for taxable duty and the ace of spades carried an indication of the name of the printer and the fact that taxation had been paid on the cards.[d] The packs were also sealed with a government duty wrapper.

## Size of the cards

Manufacturer

Country

Marketed for

Length

Width

in

mm

in

mm

Ravensburger

Germany

Poker

3.6

92

2.3

59

Handa (wide)[e]

Denmark

not specified

3.6

91

2.4

62

ASS Altenburger

Germany

Poker, Rummy

3.6

91

2.3

59

Kem (wide)

US

Poker[f]

3.5

89

2.5

64

Piatnik (narrow)

Austria

Bridge, Poker, Whist

3.5

89

2.3

58

Kem (narrow)

US

Bridge

3.5

89

2.25

57

Piatnik (wide)

Austria

Classic Poker, Poker Pro

3.5

88

2.5

63

Waddingtons

UK

not specified

3.5

88

2.3

58

Handa (narrow)

Denmark

not specified

3.4

87

2.2

56

Oberg

Sweden

Poker

3.4

87

2.2

56

Bicycle

US

Poker

3.5

88

2.5

63

Standard playing cards are available in various sizes, sometimes designated as “wide” and “narrow” or referred by the manufacturer as either “poker” or “bridge” sized;[5] nominal dimensions are summarized in the adjacent table. However, there is no formal requirement for precise adherence and minor variations are produced by various manufacturers in different countries.[6] In Germany, for example, standard Poker and Rummy packs by ASS Altenburger and Ravensburger measure 92 × 59 mm.[7] Austria’s Piatnik sells packs marketed for Bridge, Poker and Whist measuring 89 × 58 mm;[8] while Britain’s Waddingtons produce generic packs sized at 88 × 58 mm.

The slightly narrower cards are more suitable for games such as bridge and some types of poker, where a number of cards must be held or concealed in a player’s hand. In most U.S. casino poker games, plastic bridge (narrow) sized cards are used; this is for both ease of use and dealing, and the plastic cards last much longer than paper decks. U.S. casino shuffling machines have traditionally been designed for bridge-size (narrow) cards for these reasons. In other table games, such as 21 (blackjack), a modern casino may use hundreds or even thousands of decks per day, so paper cards are used for those, for economic reasons. Poker-size (wide) paper decks are used for 21 and other similar games. Other sizes are also available, such as a smaller ‘patience’ size (usually 1 3⁄4 × 2 3⁄8 in or 44 × 60 mm) and larger ‘jumbo’ ones for card tricks.

The thickness and weight of modern playing cards are subject to numerous variables related to their purpose of use and associated material design for durability, stiffness, texture and appearance.[9]

## Markings

Some decks include additional design elements. Casino blackjack decks may include markings intended for a machine to check the ranks of cards, or shifts in rank location to allow a manual check via an inlaid mirror. Many casino decks and solitaire decks have four indices instead of just two. Some modern decks have bar code markings on the edge of the face to enable them to be sorted by machine (for playing duplicate bridge, especially simultaneous events where the same hands may be played at many different venues). Some decks have large indices for clarity. These are sometimes sold as ‘seniors’ cards’ for older people with limited eyesight, but may also be used in games like stud poker, where being able to read cards from a distance is a benefit and hand sizes are small.

## Four-colour packs

Main article: Four-colour pack

The standard French-suited pack uses black for the spades and clubs, and red for the hearts and diamonds. However, some packs use four colours for the suits in order to make it easier to tell them apart. There are several schemes: a common one is the English Poker format with black spades (♠), red hearts (♥), blue diamonds (♦) and green clubs (♣). Another common system is based on the German suits and uses green spades (♠) and yellow diamonds (♦) with red hearts (♥) and black clubs (♣).

## Nomenclature

When giving the full written name of a specific card, the rank is given first followed by the suit, e.g., “ace of spades” or “Ace of Spades”.[g] Shorthand notation may reflect this by listing the rank first, “A♠”; this is common usage when discussing poker; but it is equally common in more general sources to find the suit listed first, as in “♠K” for a single card or “♠AKQ” for multiple cards. This common practice when writing about bridge as it helps differentiate between the card(s) and the contract (e.g. “4♥”, a contract of four hearts). Tens may be either abbreviated to T or written as 10.

## Terminology

Common collective and individual terms for playing cards relevant, but not exclusive to, the 52-card pack are:

Face cards or court cards – jacks, queens and kings.

Honour cards – aces and the face cards

Wild cards – When deciding which cards are to be made wild in some games, the phrase “acey, deucey or one-eyed jack” (or “deuces, aces, one-eyed faces”) is sometimes used, which means that aces, twos, and the one-eyed jacks are all wild.

Numerals or pip cards are the cards numbered from 2 to 10.

“2” cards are also known as deuces.

“3” cards are also known as treys.

“4” cards are also known as sailboats

“8” cards are also known as snowmen

## Nicknames

For a comprehensive list of card nicknames, see List of playing-card nicknames.

One-eyed Royals – the jack of spades and jack of hearts (often called the “one-eyed jacks”[10]) and the king of diamonds are drawn in profile; therefore, these cards are commonly referred to as “one-eyed”. The rest of the courts are shown in full or oblique face.

The jack of diamonds is sometimes known as “laughing boy”.[10]

Suicide kings – The king of hearts is typically shown with a sword behind his head, making him appear to be stabbing himself. Similarly, the one-eyed king of diamonds is typically shown with an ax behind his head with the blade facing toward him. These depictions, and their blood-red colour, inspired the nickname “suicide kings”.[10]

The king of diamonds is traditionally armed with an ax, while the other three kings are armed with swords; thus, the king of diamonds is sometimes referred to as “the man with the axe”. This is the basis of the trump “one-eyed jacks and the man with the axe”. Poker may be played with wild cards, often “Aces, Jacks, and the King with the Axe”.[10]

The ace of spades, unique in its large, ornate spade, is sometimes said to be the death card or the picture card, and in some games is used as a trump card.[10]

The queen of spades usually holds a sceptre and is sometimes known as “the bedpost queen”, though more often she is called the “black lady”. She also is the only queen facing left.[10]

In many decks, the queen of clubs holds a flower. She is thus known as the “flower queen”, though this design element is among the most variable; the Bicycle Poker deck depicts all queens with a flower styled according to their suit.[10]

## Combinations

It has been shown that because of the large number of possibilities from shuffling a 52-card deck (52!, equaling roughly 8.0658×1067 or 80,658 vigintillion possibilities), it is probable that no two fair card shuffles have ever yielded exactly the same order of cards.[11]

## Unicode

As of Unicode 7.0, playing cards are now represented. Note that the following chart (“Cards”, Range: 1F0A0–1F0FF) includes cards from the Tarot Nouveau deck, as well as the standard 52-card deck.

Playing Cards[1][2]Official Unicode Consortium code chart (PDF)

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

U+1F0Ax

🂠

🂡

🂢

🂣

🂤

🂥

🂦

🂧

🂨

🂩

🂪

🂫

🂬

🂭

🂮

U+1F0Bx

🂱

🂲

🂳

🂴

🂵

🂶

🂷

🂸

🂹

🂺

🂻

🂼

🂽

🂾

🂿

U+1F0Cx

🃁

🃂

🃃

🃄

🃅

🃆

🃇

🃈

🃉

🃊

🃋

🃌

🃍

🃎

🃏

U+1F0Dx

🃑

🃒

🃓

🃔

🃕

🃖

🃗

🃘

🃙

🃚

🃛

🃜

🃝

🃞

🃟

U+1F0Ex

🃠

🃡

🃢

🃣

🃤

🃥

🃦

🃧

🃨

🃩

🃪

🃫

🃬

🃭

🃮

🃯

U+1F0Fx

🃰

🃱

🃲

🃳

🃴

🃵

Notes

1.^ As of Unicode version 13.0

2.^ Grey areas indicate non-assigned code points

## See also

500 decks come with extra ranks.

French playing cards

German playing cards

Italian playing cards

Spanish playing cards

Stripped decks come with fewer ranks.

Tarot Nouveau, the most common French-suited tarot game deck

## Notes

^ 52 cards excluding any Jokers.

^ ‘Deck’ and ‘pack’ are synonymous; ‘deck’ tends to be used in America and ‘pack’ elsewhere.

^ ‘English pattern’ is the name recommended by the IPCS.

^ The Stamp Act 1765 imposed a tax on playing cards.

^ Taken from a pack with a tourist motif, so may have been aimed at American market.

^ Kem Poker cards are close to the B8 (88 x 62 mm) size of ISO 216.

^ Sources vary as to the capitalisation used with American sources tending to favour lower case and British sources tending towards capitals, but there are numerous exceptions and some sources combine them e.g “Ace of spades”.

## References

^ a b Pattern Sheet 80 at i-p-c-s.org. Retrieved 23 August 2020.

^ McLeod, John. Games played with French suited cards at pagat.com. Retrieved 17 April 2017.

^ French regional pattern sheets and French non-regional pattern sheets at i-p-c-s.org. Retrieved 17 April 2017.

^ a b c .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:”\”””\”””‘””‘”}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg”)right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}”The English pattern”. International Playing-Card Society. Retrieved 17 April 2017.

^ Kem Cards official website. Narrow (Bridge) Size verses Wide (Poker) Size, retrieved 2014-02-27.

^ In a sample of 95 American bridge and poker card sets, lengths ranged from 87.50 mm to 89.50 mm. In a sample of 28 bridge sized cards, widths varied from 56.98 mm to 58.25 mm. In a sample of 67 poker sized cards, widths varied from 62.44 to 63.54 mm. Reference: Home Poker Tourney website. Playing Card Review, retrieved 2014-02-27.

^ Poker at ravensburger.de. Retrieved 21 August 2020.

^ Bridge – Poker – Whist at piatnik.com. Retrieved 21 August 2020.

^ In a sample of 28 bridge-sized cards, the weight of a card varied from 1.8 g to 2.48 g and thickness from 0.26 mm to 0.34 mm. In a sample of 67 poker-sized cards, the weight of a card varied from 1.4 g to 2.78 g and thickness from 0.24 mm to 0.34 mm. Reference: Home Poker Tourney Web site. Playing Card Review, retrieved 2014-02-27.

^ a b c d e f g Common Playing Card Nicknames at playingcarddecks.com. Retrieved 10 November 2020.

^ “The Amazing Truth About a Deck of Cards”. KnowledgeNuts.

vtePlaying cardsStandard52-card pack

Suit/rank

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2

Spades ♠

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2

Hearts ♥

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2

Diamonds ♦

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2

Clubs ♣

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2

Other packs

Piquet pack

French pack

German pack

Italian pack

Spanish pack

Swiss pack

Tarot pack

Four-colour packOther cards

Banner

Blank

Face card/Court card (Knight, Ober, Unter)

Pip card (Deuce, Weli)

Joker

Card nicknames

Stripped deck

Talon

UnicodeOther suits

German: Acorns

Leaves

Hearts

Bells

Swiss: Acorns

Shields

Roses

Bells

Latin (Italian/Spanish): Cups

Coins

Batons

Swords

vtePlaying card decksItalicized are not used for games at presentBy suit-systemFrench

Standard 52-card deck

500

Four-color deck

Russian

Adler-Cego

Industrie und Glück

Tarot NouveauGerman

German

Northern

Southern

Württemberg

William Tell

SwissLatin

Italian

Tarocco Bolognese

Tarocco Piemontese

Swiss 1JJ

Tarot of Marseilles

Tarot de Besançon

Trappola

Spanish

Aluette

Portuguese

Tarocco Siciliano

MinchiateSingle-suited

As-Nas

Gnav

KvitlechBy geography

Chinese

Zi pai

Chess-suited: Four Color Cards, Tam cúc

Money-suited: Madiao, Tổ tôm

Ganjifa

Dashabatar Cards

Ganjapa

Karuta

Hanafuda

Kabufuda

Uta-garuta

Tujeon

vteNon trick-taking card games

Shuffling

Cutting

Glossary of card game termsAdding

Cribbage

Costly Colours

Ninety-nine

NoddyCollecting

Beggar-my-neighbour

Egyptian Ratscrew

My Ship Sails

Ninety-nine

Ochse, leg dich!

Quartets

Schlafmütze

WarCommerce

Brag

Commerce

James Bond

Kemps

Schwimmen

Stop the BusCompendium

Barbu

Bauernfangen

Bonken

Dreeg

Herzeln

Kein Stich

King

Lorum

Poch

Quodlibet

Rosbiratschka

TrexDraw and discard

Buraco

Colonel

Canasta

Carioca

Continental Rummy

Contract Rummy

German Rummy

Golf

Kalooki

Militaire

Robbers’ rummy

Rummy

Gin rummy

Rumino

Thirty-one

Three Thirteen

Tonk

Treppenrommé

Viennese Rummy

Yaniv

500 RumFishing

Bastra

Byggkasino

Cassino

Cicera

Cuarenta

Escoba

Pasur

Go-Stop

Mulle

Scopa

Skwitz

Tablanette

ZwickerMatching

Kings in the Corner

Lusti-Kartl’n

Nain Jaune

Newmarket

Poch

Ristikontra

Sedma

Sedmice

Snip-Snap-SnorumShedding

Bartok

Big two

Craits

Crazy Eights

Cheat

Daifugō

Dou dizhu

Dupa biskupa

Durak

Hund

Irish switch

Jack Change It

Kille

Last Card

Mao

Mau-Mau

One-card

Paskahousu

President

Ranter-Go-Round

Quatorze

Ristiseiska

Shithead

Spit

Switch

{{Historical card games}} {{Trick-taking card games}} {{Tarot and Tarock card games}}

Retrieved from “https://en.wikipedia.org/w/index.php?title=Standard_52-card_deck&oldid=1017407023”

A standard deck of cards contains 52 cards. One card is selected… – One card is selected from the deck.? (a)Compute the probability of randomly selecting a diamond or club. You have a deck of 52 cards you pick one what would be the probability that you would pick a spade.The standard 52-card deck of French-suited playing cards is the most common pack of playing cards used today. In English-speaking countries it is the only traditional pack used for playing cards…First off, this is a combinations question – we don't care about the order in which the cards are dealt. So of those nearly 2.6 million hands, how many are 2 pair hands? To achieve 2 pair, we first need to select, from the 13 ordinals (Ace through 10, Jack, Queen, King) 2 of them

Standard 52-card deck – Wikipedia – A standard deck of cards is a widely used sample in basic probability. The deck will have 52 cards divided into 4 suits and 13 ranks. The deck does not include any jokers. Probability Examples. The above information comes in handy when it's time to calculate probabilities with a standard deck of…a standard 52-card deck. What is the probability of drawing a 7? Ex: Find Basic Probabilities Using a Deck of Playing Cards. In many decks, the queen of clubs holds a flower. She is thus known as the "flower queen", though this design element is among the most variable; the Bicycle Poker deck…One card is selected from the deck.A standard deck of cards contains 52 cards. Can someone please help me with this: A standard deck of cards contains 52 cards.

Consider a standard deck of 52 cards. How many 5 card… | Socratic – Three cards are drawn one at a time from a standard deck of cards without replacement. You have 3 cards which are a heart AND a face card, so you need to subtract 3/52 from the answer. Is a card drawn at random from the deck, or is the person able to look at the faces of the cards while doing…A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Modern decks also usually include two Jokers.Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. In how many ways 5 cards can be selected from a "standard" deck of playing cards, without a replacement, so that all As cards had to be replaced at any moment there are 52 cards in the deck i.e. 13 cards in each suit.

**Probability of 5 Card Hands Using Combinations: Part 1** – Five cards are drawn randomly from a standard deck of 52 cards.

We're asked to give each

probability as a percentage to four decimal places, which means we'll first

find the probability to six decimal places and

then convert to a percentage. We're first asked to find the probability that exactly three cards are kings. We need to be careful here, because if exactly three cards are kings, then we also have two

cards that are not kings, because we are drawing five cards. The probability of an event is equal to the favorable number of outcomes divided by the total number of outcomes. Let's beginning by

determining the total number of possible outcomes

when drawing five cards from a deck of 52 cards. Because the order does not matter, the number of ways of selecting five cards from 52 cards is 52 choose five. Again we use a combination because the order does not matter. And now the favorable number of outcomes is going to be the number of ways we can select three kings from the kings in the deck and then times the number of ways we can select two cards that

are not kings from the deck. And there are four kings in a deck and therefore the number

of ways of selecting three kings from four

kings is four choose three and then we have times the number of ways we can select two cards from

the deck that are not kings. Well if there are four kings in the deck, then there must be 52 minus four or 48 cards that are not kings. And therefore the number

ways of selecting two cards that are not kings is 48 choose two. So the number of favorable outcomes is equal to four choose

three times 48 choose two. And let's evaluate this on the calculator. And again we'll have to get the decimal to six decimal places so the percentage is accurate

to four decimal places. We need the numerator in parentheses, so we have open parenthesis

four choose three, right arrow times 48 choose two, right arrow, closed parenthesis, and this is divided by, in

parentheses, 52 choose five, which to six decimal places

is approximately 0.001736. Which as a percentage is 0.17336%. Next we're asked to find the probability that all five cards are hearts. And again the total number of outcomes is going to be 52 choose five. The favorable number of outcomes is equal to the number of

ways we can select five hearts from the hearts in the deck and since there are 13 hearts in the deck, the number of ways of selecting

five hearts from 13 hearts is 13 choose five. And this does accommodate for

all five cards being drawn and therefore this quotient

is the probability. So going back to the calculator we have 13 choose five, divided by 52 choose five. Notice how this is giving

us scientific notation. This means 4.95 et cetera times 10 raised to the power of negative four. To convert to a decimal, we move the decimal point

four places to the left which'll give us 0.000495

to six decimal places. Which is equal to 0.0495%. Again, the calculator gave us approximately 4.95 times

10 to the negative four which is equal to 0.000495. Notice how to go from scientific notation to decimal notation you

move the decimal point four places to the left, because the exponent was negative four. For the last example we'll

asked to find the probability that exactly four cards are face cards, which means four cards will be face cards and one card will not be a face card. The total number of possible outcomes is still going to be 52 choose five. And now for the favorable outcomes, let's first determine how many ways we can select four face cards from the 12 face cards in the deck. Because there are 12

face cards in the deck, the number of ways of

selecting four face cards is 12 choose four. We have to multiply this by the number of ways of selecting one card that is not a face card. And the number of cards

that are not face cards is equal to 52 minus 12 of 40. And therefore the number of ways of selecting one card

that is not a face card is 40 choose one. And now let's go back to the calculator. So in parentheses, we have 12 choose four times 40 choose one divided by 52 choose five. And now see this isn't correct because I forgot to divide here, so I'll press second enter to bring up these previous entry. Move the cursor to here and press

second, delete for insert and then divide and then press enter. So to six decimal places we

have approximately 0.007618, which as a percentage is 0.7618%. I hope you found this helpful. .

**Four cards are drawn at random from a pack of 52 cards** – .

**HW – 5.2 – 04** – We're looking at homework for section 5.2.

This is question #4. It's a multipart question. In a survey of a group of men, the Heights in the 20 to 29 age group were normally distributed with a mean of 68.7 inches in a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts A through D below. So we'll start with part A. Find the probability that a study participant has a height that is less than 67 inches. So we have to find our Z score for X equals 67. The Z score formula is Z equals X minus mu over Sigma. So in this context it would be 67 – 68.7 over 4. 67 – 68.7 is -1.7 over 4. Which ends up being -.425 we're going to round to two decimal places because the Z scores in our standard normal distribution table are two decimal place Z scores, so this would round to-0.43. Since that's a negative Z score, we're going to need the negative side of the standard normal distribution table. We look up Z equals -.43 and we find our table value which ends up being our area of .3336. So the probability that X is less than 67 is going to be .3336. So that's your answer for part A. For Part B. Find the probability that a study participant has a height that is between 67 and 70 inches. So we already found the Z score that was associated with the X equals 67. So let's go ahead and find the Z score for X equals 70. When X equals 70, we use X minus mu over Sigma, so that's going to be 70 – 68.7 over 4. Which is 1.3 over 4. Which is .325 rounded to two decimal places is 0.33. So that means we need the positive side of the standard normal distribution table. So our table value here is going to be .6293. And then our probability. We can use the value from part A along with this value we just found for X equals 70. And it's going to be .6293 minus the .3336. From part A, because we always do the table value that's furthest right minus the table value on the left. And when we do the subtraction, we end up with .2957. And that is your answer for Part B. For part C. We're looking to find the probability that a study participant has a height that is more than 70 inches. So we've already computed the Z score for X equals 70. It was Z equals .33. So because this is a greater than area. A greater than probability. Then we do 1 minus the table value for that Z score. And we get. 1 – .6293. Which gives us an area of .3707 and that area is equal to the probability. So the probability that X is greater than 70 is .3707 Now we're ready to answer Part D. Identify any unusual events. Well, remember an unusual event would be an event that had a probability that was less than .05. So when you look back at parts A, B & C, none of those were less than .05, so there are no unusual events. And that's your answer. .