What is the probability of not picking a king if you choose randomly from a pack of 52 cards?
Last Updated : 24 Sep, 2024
In one pack of cards, there are 4 kings in a deck of 52,
therefore , the probability of drawing a king is = Probability of an event, P(A)
= Favorable outcomes / Total number of outcomes
= 4/52
= 1/13
Hence, the probability of not picking a king P(B) = 1 - P(A)
= 1 - 1/13
= 12/13
Therefore the probability of not picking a king if you choose randomly from a pack of 52 cards is 12/13
Probability of event A is generally written as P(A). Here, P represents the possibility and A represents the event. 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 the event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
If not sure about the outcome of an event, take help of the probabilities of certain outcomes, and how likely they occur. For a proper understanding of probability, take the example of tossing a coin, there will be two possible outcomes - heads or tails.
Formula of Probability
Probability of an event, P(A) = Favorable outcomes / Total number of outcomes
Choosing a random card from a Deck of Cards:
It is known that a well-shuffled deck has 52 cards, therefore the Total number of cards is 52. All the cards are further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each. Each suit has 13 cards (A, 2 to 10, Jack, Queen, King). So, the total number of outcomes will be 52. Out of 52, King, Queen, and Jack (or Knaves) are face cards. In total, there are 12 face cards in the deck of 52 playing cards.
With the formula of probability, we can find the probability of the random card picked from the deck of 52:
Probability of an event, P(A) = Favorable outcomes / Total number of outcomes.
Example: What is the probability of having the number 4 card picked from the deck of 52 cards?
Solution:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
probability of getting 4 = 4
Total number of outcomes =52
so probability of having number 4 card is = Probability of an event, P(A)
= Favorable outcomes / Total number of outcomes.
= 4/52
= 1/13
Similar Questions
Question 1: What is the probability of getting either a heart or a jack when drawing a single card from a deck of 52 cards?
Solution:
It is known that a well-shuffled deck has 52 cards
Total number of black cards = 26
Total number of red cards = 26
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
probability of getting either a heart or a jack?
probability of getting a heart = 13
probability of getting a jack = 4
And probability of getting a jack of heart = 1
Therefore probability of getting a heart = {total number of heart cards in the deck}/{total number of cards in the deck}
= 13/52
Probability of getting a heart = 1/4
And the probability of getting either a jack = {total number of jack cards in the deck}/{total number of cards in the deck}
= 4/52
Probability of getting a jack = 1/13
probability of getting a jack of heart = {total number of jack of heart in the deck}/{total number of cards in the deck}
= 1/52
Question 2: What is the probability of getting a queen?
Solution:
Total number of cards are 52
number of queens are 4
So, total outcomes = 52
favorable outcomes = 4
So, the probability of getting a queen = Favorable outcomes / Total outcomes
= 4 / 52
P = 1/13
therefore the probability of getting queen is 1/13
Question 3: What is the probability of drawing a red card from a well-shuffled deck of 52 cards?
Solution:
We know that a well-shuffled deck has 52 cards
Total number of black cards = 26
Total number of red cards = 26
Therefore probability of getting a red card = {total number of red cards in the deck}/{total number of cards in the deck}
= 26/52
= 1/2
So the probability of having red card is 1/2
Question 4: What is the probability of getting a black queen?
Solution:
Total number of cards = 52
Number of favorable cards that are black queen = 2
so, probability of getting a black queen = 2/52
Therefore, probability of getting a black queen = 2/52
P(E) = probability of getting a black queen
= 2/52
= 1/26
so the probability of getting a black queen is 1/26
Question 5: What is the probability of getting a queen of spades?
Solution:
Total number of cards = 52
Total spades cards are 13 ..
Number of favorable cards that are queen of spades = 1
so, probability of getting a spade queen = 1/52
Therefore, probability of getting a spade queen = 1/52
P(E) = probability of getting a spade queen
= 1/52
so the probability of getting a spade queen is 1/52
Question 6: What is the probability of having a 4 of diamond card?
Solution:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of outcome = 52
number of favorable outcome of having 4 of diamond card = 1
therefore the probability of having 4 of diamond card = number of favorable outcome / total number of outcome
= 1/52
= 1/52
Question 7: What is the probability of getting a black face card?
Solution:
It is known that a well-shuffled deck has 52 cards
Total number of cards = 52
further divided into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each.
And Each suit has 13 cards (A, 2 to10, Jack, Queen, King).
So , total number of black cards = 13 of spades and 13 of clubs = 26
out of these 26 black cards total face cards are = 6
number of favorable outcome of having black face card = 6
therefore the probability of having 4 of diamond card = number of favorable outcome / total number of outcome
= 6/52
= 3/26
Probability calculation:
Total cards: 52
Number of kings: 4
Probability of not picking a king = (52 - 4) / 52 = 48/52 = 12/13 ≈ 0.9231 or about 92.31%
Summary
The probability of not picking a king when randomly selecting a card from a standard 52-card deck is 48/52, which simplifies to 12/13. This can be expressed as approximately 0.9231 or 92.31%. In other words, you have a high chance of not picking a king in a single random draw.