Question

From a well shuffled pack of cards, one card is drawn at random. The probability that the card is drawn is an ace is:
A. \[\dfrac{1}{{13}}\]
B. \[\dfrac{4}{{13}}\]
C. \[\dfrac{3}{{52}}\]
D. None of these

Answer 1

Hint: The sample space for a set of cards is \[52\] as there are \[52\] cards in a deck. There are \[4\] Aces in every deck, \[1\] of every suit. Probability of any event can be between \[0\]and \[1\] only.
Probability (event) \[ = \dfrac{{Number\;of\;favourable\;outcomes}}{{Total\;n umber\;of\;outcomes}}\]

Complete step by step answer:
Before we proceed to the solution, you must be familiar with all the terms related to playing cards.
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.
There are two colors of cards in each deck:
Red
Black
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.
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:
Spades
Hearts
Diamonds
Clubs
There are \[52\] cards in a deck.
Each card can be categorized into \[4\] suits constituting \[13\] cards each.
There is one more categorization of a deck of cards:
Face cards
Number cards
Aces
Face Cards
These cards are also known as court cards.
They are Kings, Queens, and Jacks in all \[4\] suits.
Number Cards
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.
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 the same in every pack of \[52\] cards.
Therefore , probability(Ace) \[ = \dfrac{{Number\;of\;favourable\;outcomes}}{{Total\;n umber\;of\;outcomes}}\]
 \[ = \dfrac{4}{{52}}\]
 \[ = \dfrac{1}{{13}}\]

So, the correct answer is “Option A”.

Note: The sample space for a set of cards is \[52\] as there are \[52\] cards in a deck. Probability of any event can be between \[0\]and \[1\] only. Probability of any event can never be greater than \[1\]. Probability of any event can never be negative.