What is the probability of drawing a jack of hearts from a deck of 52 cards?

Hint- Here, we will be using the general formula for finding the probability of occurrence of an event.

Given, one card is drawn from a well-shuffled deck of 52 cards
Total number of cards$ = 52$
As we know that the general formula for probability is given by
Probability of occurrence of an event $ = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$
$\left( {\text{i}} \right)$ In this case, the favorable event is drawing a king of red colour from the deck of 52 cards.
Since we know that in a deck of 52 cards, there are 2 kings of red colour (one king of diamond and the other king of heart).
Number of kings of red colour$ = 2$
Therefore, probability of getting a king of red colour $ = \dfrac{{{\text{Number of kings of red colour}}}}{{{\text{Total number of cards}}}} = \dfrac{2}{{52}} = \dfrac{1}{{26}}$
$\left( {{\text{ii}}} \right)$ In this case, the favorable event is drawing a face card (king, queen or jack) from the deck of 52 cards.
Since we know that in a deck of 52 cards, there are a total 12 face cards (3 face cards each of heart, diamond, spade and club).
Number of face cards$ = 12$
Therefore, probability of getting a face card$ = \dfrac{{{\text{Number of face cards}}}}{{{\text{Total number of cards}}}} = \dfrac{{12}}{{52}} = \dfrac{3}{{13}}$.
$\left( {{\text{iii}}} \right)$ In this case, the favorable event is drawing a red face card (king, queen or jack) from the deck of 52 cards.
Since we know that in a deck of 52 cards, there are a total 6 red face cards (3 face cards of heart and 3 face cards of diamond).
Number of face cards$ = 6$
Therefore, probability of getting a red face card$ = \dfrac{{{\text{Number of red face cards}}}}{{{\text{Total number of cards}}}} = \dfrac{6}{{52}} = \dfrac{3}{{26}}$.
$\left( {{\text{iv}}} \right)$ In this case, the favorable event is drawing a jack of hearts card from the deck of 52 cards.
Since we know that in a deck of 52 cards, there is only 1 jack of hearts card.
Number of jack of hearts card$ = 1$
Therefore, probability of getting a jack of hearts card$ = \dfrac{{{\text{Number of jack of hearts card}}}}{{{\text{Total number of cards}}}} = \dfrac{1}{{52}}$.
$\left( {\text{v}} \right)$ In this case, the favorable event is drawing a spade card from the deck of 52 cards.
Since we know that in a deck of 52 cards, there are 13 spade cards.
Number of spade cards$ = 13$
Therefore, probability of getting a spade card$ = \dfrac{{{\text{Number of spade cards}}}}{{{\text{Total number of cards}}}} = \dfrac{{13}}{{52}} = \dfrac{1}{4}$.
$\left( {{\text{vi}}} \right)$ In this case, the favorable event is drawing a queen of diamonds card from the deck of 52 cards.
Since we know that in a deck of 52 cards, there is only 1 queen of diamonds card.
Number of queen of diamonds card$ = 1$
Therefore, probability of getting a queen of diamonds card$ = \dfrac{{{\text{Number of queen of diamonds card}}}}{{{\text{Total number of cards}}}} = \dfrac{1}{{52}}$.

Note- In these types of problems, we should know that in a deck of 52 cards there are 13 cards each of heart, diamond, spade and club. 13 cards of heart and 13 cards of diamond are red in colour whereas 13 cards of spade and 13 cards of club are black in colour. In these pairs of 13 cards there are 3 face cards consisting of a king, a queen and a jack.

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Question 209229: A single card is drawn from an ordinary 52-card deck. Find the probability of getting a heart and a jack.
Answer by Theo(12415)   (Show Source):

You can put this solution on YOUR website!
number of hearts in the deck is 13
number of jacks in the deck is 4
one of those jacks is a heart so the number of jacks in the deck that is not a heart is 3.
13 hearts plus 3 jacks makes a total of 16 cards that are either a heart or a jack.
the probability of drawing a jack OR a heart on one draw of the cards is 16/52
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you said, however, what is the probability of drawing a jack AND a heart.
there is only 1 jack of hearts in the deck, so the probability is 1/52 that you will get a heart and a jack on one draw of the cards.
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The probability that any specific card is any specific value is $\frac 1{52}$. It doesn't matter if it is the first card, the last card, or the 13th card. So the probability that the second card is the Jack of Hearts is $\frac 1{52}$. Picking the first card and not looking at, just going directly to the second card, putting the second card in an envelope and setting the rest of the cards on fire, won't make any difference; all that matters is the second card has a one in $52$ chance of being the Jack of Hearts.

Any thing else just wouldn't make any sense.

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The thing is throwing in red herrings like "what about the first card?" doesn't change things and if you actually do try to take everything into account, the result, albeit complicated, will come out to be the same.

What is the probability of getting a jack of hearts from 52 cards?

How many Jack of Hearts cards in a deck of 52?