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What is the probability of choosing a King, Queen or Jack of Hearts from a deck of 52 cards?

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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 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, how likely they occur. For a proper understanding of probability, take an 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.

And Each suit has 13 cards (A, 2 to10, Jack, Queen, King). So, the total number of outcomes will be 52. Out of 52, King, Queen and Jack (or Knaves) are face cards. 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 number 2 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 2 = 4 

Total number of outcomes = 52

so probability of having number 2 card is = Probability of an event, P(A) 

                                                                  = Favorable outcomes / Total number of outcomes.

                                                                  = 4/52

                                                                  = 1/13 

What is the probability of choosing a King, Queen or Jack of Hearts from a 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 king of heart        = 1/13

probability of getting a queen of heart  = 1/13

probability of getting a jack of heart      = 1/13

Therefore probability of getting a  king , queen or jack heart = {probability of getting king of heart + probability of getting a queen of heart + probability of getting a jack of heart}

= 1/13 + 1/13 + 1/13

Probability of getting a king, queen or jack heart = 3/13

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 not picking a king if you choose randomly from a pack of 52 cards?

Solution: 

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 

Question 3: What is the probability of getting a king or a red card?

Solution:

Total number of cards are 52

number of red cards are 26 and kings are 4 whereas 26 red cards contain 2 kings (so only 2 will be considered out of 4).

So, total outcomes = 52

favorable outcomes = 26 + 2 = 28

So, the probability of getting a king or red card = Favorable outcomes / Total outcomes

                                                                          = 28 / 52 = 7/13

                                                                       P = 7/13

Therefore the probability of getting a king or a red card is 7/13

Question 4: Find the probability of getting a number less than 3 in a single dice throw.

Solution:

When the dice is rolled then there will be 6 outcomes.

Total number of favorable outcome {set of outcome} = {1, 2, 3, 4, 5, 6}

                                                                                  = 6

Now as per the question,

Probability of getting a number less than 3 in a single throw is 2

Numbers less than 3 are {1,2}

therefore favorable outcome will be = 2

P(A) = Favorable outcomes / Total number of outcomes

        = 2/6

        = 1/3

Hence the probability of getting a number less than 3 in a single throw of a die is 1/3

Question 5: A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting 3 of spades?

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 3 of spades = 1

therefore the probability of getting 3 of spades   =  number of favorable outcome / total number of outcome

                                                                             = 1/52

Question 6: What is the probability of having a jack 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 jack = 4

therefore the probability of having jack card  = number of favorable outcome / total number of outcome

                                                                         = 4/52

                                                                         = 1/13

Question 7: What is the probability of having 3 of hearts?

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 3 of heart = 1

therefore the probability of having jack card  = number of favorable outcome / total number of outcome

                                                                       = 1/52

                                                                       = 1/52



Last Updated : 08 Mar, 2022
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