What is the probability of getting a queen of spades in a deck of 52 cards?

Playing card

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Roles by game
Card reading
Similar Questions

Q♠ in a standard deck

Pallas, Q♠ in the Paris pattern[1][2]

Q♠ in a Russian deck

Q♠ from 19th-century tarock deck

The queen of spades (Q♠) is one of 52 playing cards in a standard deck: the queen of the suit of spades (♠). In Old Maid and several games of the Hearts family, it serves as a single, undesirable card in the deck.

Roles by game

In the Hearts family of card games, the queen of spades is usually considered an unlucky card; it is the eponym of the Black Maria and Black Lady variants of Hearts. The player who ends up with the queen of spades after a match scores 13 points (points are to be avoided in this game). The exception is when the player receives this card with all 13 hearts, in which the player is said to have shot the moon, and this player scores no points, while all opponents are scored 26 points.

In the game of Old Maid, while any card can technically be used for this purpose, the queen of spades is traditionally used as a card that has no match, thereby making it the "old maid" card.

In the seven card stud poker variant known as "The Bitch", a face-up deal of the queen of spades results in the deal being abandoned, all cards being shuffled and a new deal starting with only those players who had not already folded when the queen of spades was dealt.[3]

In Pinochle, the queen of spades and the jack of diamonds combine for a unique two-card meld known as a "pinochle".

Card reading

In cartomancy, the queen of spades is considered to be a sign of intelligence. It is representative of judgment that is practical, logical, and intellectual. It represents a woman who is creative and makes her plans ahead of time.[4]

References

Wikimedia Commons has media related to Queens of Spades.

^ "The Four King Truth" at the Urban Legends Reference Pages
^ Who are the court figures? at the International Playing-Card Society. Retrieved 22 October 2016.
^ "Rules of Poker Variants: Chicago, Black Mariah, The Bitch". www.pagat.com. Retrieved 21 August 2020.
^ Jones, Marthy (1984). It's in the cards. York Beach, Me: S. Weiser. ISBN 978-0-87728-600-4. OCLC 11357269. Translation of: In de kaart gekeken.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Queen_of_spades&oldid=1101251594"

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You deal 5 cards from a well-shuffled deck of playing cards. What is the probability that the 5th card is the queen of spades?

Just from analysis, P(5th queen spade) = (51*50*49*48*1)/(52*51*50*49*48) = 1/52

However why wont this method of logic thinking incorrect?

P(5th queen spade) = (51Cr4) / (52Cr5) = 5/52. Reasoning: choose any first 4 cards and last card is queen spade, divide by all possible choice

Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.

So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

Note: If the probability of occurring of an event A is 1/3 then the probability of not occurring of event A is 1-P(A) i.e. 1- (1/3) = 2/3

What is Sample Space?

All the possible outcomes of an event are called Sample spaces.

Examples-

A six-faced dice is rolled once. So, total outcomes can be 6 and
Sample space will be [1, 2, 3, 4, 5, 6]
An unbiased coin is tossed, So, total outcomes can be 2 and
Sample space will be [Head, Tail]
If two dice are rolled together then total outcomes will be 36 and
Sample space will be [ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

Types of Events

Independent Events: If two events (A and B) are independent then their probability will be

P(A and B) = P (A ∩ B) = P(A).P(B) i.e. P(A) * P(B)

Example: If two coins are flipped, then the chance of both being tails is 1/2 * 1/2 = 1/4

Mutually exclusive events:

If event A and event B can’t occur simultaneously, then they are called mutually exclusive events.
If two events are mutually exclusive, then the probability of both occurring is denoted as P (A ∩ B) and
P (A and B) = P (A ∩ B) = 0
If two events are mutually exclusive, then the probability of either occurring is denoted as P (A ∪ B)
P (A or B) = P (A ∪ B)
= P (A) + P (B) − P (A ∩ B)
= P (A) + P (B) − 0
= P (A) + P (B)

Example: The chance of rolling a 2 or 3 on a six-faced die is P (2 or 3) = P (2) + P (3) = 1/6 + 1/6 = 1/3

Not Mutually exclusive events: If the events are not mutually exclusive then

P (A or B) = P (A ∪ B) = P (A) + P (B) − P (A and B)

What is Conditional Probability?

For the probability of some event A, the occurrence of some other event B is given. It is written as P (A ∣ B)

P (A ∣ B) = P (A ∩ B) / P (B)

Example- In a bag of 3 black balls and 2 yellow balls (5 balls in total), the probability of taking a black ball is 3/5, and to take a second ball, the probability of it being either a black ball or a yellow ball depends on the previously taken out ball. Since, if a black ball was taken, then the probability of picking a black ball again would be 1/4, since only 2 black and 2 yellow balls would have been remaining, if a yellow ball was taken previously, the probability of taking a black ball will be 3/4.

Some points related to Cards:

There are 52 cards in a deck.
In 52 cards, there are 26 cards of each color i.e. 26 red and 26 black cards.
In 26 red cards, there are 2 suits of 13 cards each i.e. 13 heart and 13 diamond cards.
In 26 black cards, there are 2 suits of 13 cards each i.e. 13 spades and 13 club cards.
Each suite has 13 cards from 2 to 10, J, Q, K, and A which means 4 cards of each type.
J, Q, and K are known as Face cards.
What is the probability of getting a queen and a jack card?

Solution:

Total number of cards are 52 and number of queens and jacks in 52 cards are 4 and 4 respectively.
So, total outcomes = 52
favorable outcomes = 4 + 4 = 8
So, the probability of getting a queen or a jack = Favorable outcomes/Total outcomes = 8/52

P(J or Q) = 2/13