When one card is drawn from a pack of 52 well shuffled card What is the probability of getting a spade?

Solution:

We use the basic formula of probability to solve the problem.

Probability = Number of possible outcomes/Total number of favorable outcomes.

Total number of cards from a well-shuffled deck = 52

Number of spade cards = 13

Number of heart cards = 13

Number of diamond cards = 13

Number of club cards = 13

Total number of kings = 4

Total number of queens = 4

Total number of jacks = 4

Number of face cards = 12

(i) Probability of getting a king of red colour = Number of red colour king/Total number of outcomes

We will have 2 red kings (Heart and Diamond)

= 2/52 = 1/26

(ii) Probability of getting a face card = Number of face cards/Total number of outcomes

12/52 = 3/13

(iii) Probability of getting a red face card = Number of red face cards/Total number of outcomes

We will have 3 diamond face cards and 3 heart face cards that sum up to 6 red face cards.

= 6/52 = 3/26

(iv) Probability of getting the jack of hearts = Number of jack of hearts/Total number of outcomes

= 1/52

(v) Probability of getting a spade card = Number of spade cards/Total number of outcomes

= 13/52 = 1/4

(vi) Probability of getting the queen of diamonds = Number of possible outcomes/Total number of favourable outcomes

= 1/52

Check out more in terms of probability.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 15

Video Solution:

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 14

Summary:

If one card is drawn from a well-shuffled deck of 52 cards, then the probability of getting (i) a king of red colour, (ii) a face card, (iii) a red face card, (iv) the jack of hearts, (v) a spade, and (vi) the queen of diamonds are 1/26, 3/13, 3/26, 1/52, 1/4, and 1/52 respectively.

☛ Related Questions:

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a spade.

Total number of cards in a well-shuffled deck = 52

Total number of spade cards = 13

P (getting a spade card) =`"Number of favourable outcomes"/"Total number of outcomes"`

= 13/52 = 1/4

Concept: Probability - A Theoretical Approach

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Page 2

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting the queen of diamonds.

Total number of cards in a well-shuffled deck = 52

Total number of spade cards = 1

P (getting a spade card) =`"Number of favourable outcomes"/"Total number of outcomes"`

= 1/52

Concept: Probability - A Theoretical Approach

Is there an error in this question or solution?

Answer

Verified

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 cardsTotal number of cards$ = 52$As we know that the general formula for probability is given byProbability 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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