Question

A WELL SHUFFLED DECK OF 52 CARD,ONE CARD DRAWN AT RANDOM.FIND THE PROBABILITY TO GET (1) A RED CARD (II) QUEEN OF HEART (III) A FACE CARD​

Answer 1

Step-by-step explanation:

Given :-

A well shuffled deck of 52 cards .

To find :-

If one card is drawn randomly then find the probability of getting the following:

1) A Red Card

2) A Queen of Heart

3) A Face Card

Solution :-

Given that :

Total number of playing cards in a deck of cards = 52

Total number of all possible outcomes = 52

Probability of getting a red card :-

Number of red cards in the deck of cards = 26

Number of favourable outcomes to red card = 26

We know that

Probability of an event P (E) = Number of favourable outcomes/ total number of all possible outcomes

Probability of getting a red card = P(R)

=> P(R) = 26/52

=> P(R)= 1/2

P(R) = 1/2

2) Probability of getting a Queen of Hearts:-

Number of Hearts cards in the deck of cards = 13

Number of Queens in hearts = 1

Number of favourable outcomes to Queen of Hearts = 1

We know that

Probability of an event P (E) = Number of favourable outcomes/ total number of all possible outcomes

Probability of getting a Queen of hearts = P(Q)

=> P(Q) = 1/52

P(Q) = 1/52

3) Probability of getting a Face Card:-

J,Q,K are called Face cards

They are in hearts = 3

They are in clubs = 3

They are in spades = 3

They are in diamons = 3

Total = 3+3+3+3 = 12

Number of face cards in the deck of cards = 12

Number of favourable outcomes to face card = 12

We know that

Probability of an event P (E) = Number of favourable outcomes/ total number of all possible outcomes

Probability of getting a face card P(F)

=> P(F) = 12/52

=> P(F) = (3×4)/(13×4)

=> P(F) = 3/13

P(F) = 3/13

Answer :-

1)Probability of getting a red card = 1/2

2)Probability of getting a Queen of hearts = 1/52

3)Probability of getting a face card = 3/13

Used formulae:-

• Probability of an event P (E) = Number of favourable outcomes/ total number of all possible outcomes

Points to know :-

• There are 52 playing cards in a deck of cards.

• They are divided into two colors . They are black (26) and Red (26)

• Black cards are divided into two suits they are Spades (13) and Clubs (13)

• Red cards are divided into two suits they are Hearts (13) and Diamonds (13)

• In every suit there are 2,3,4,5,6,7,8,9,10, A,J,Q,K

• Clubs - (♣), diamonds -(♦), hearts- (♥) and spades- (♠)