Question

16. A card is drawn from a well shuffled pack of 52 playing card, find the probability of getting

(i) An ace

(ii) A red card

(iii) A face card

(iv) A card of heart

(v) Neither King nor Queen

​

Answer 1

Card structure

• Total number of card = 52
• Card is divided into four suits: Clubs, Diamonds, Hearts, and Spades.
• Each suit has 13 cards.

• Each suit has thirteen cards: Ace - Two - Three - Four - Five - Six - Seven - Eight - Nine - Ten - Jack - Queen - King.
• Diamond and Hearts are the red card.
• Clubs and Spades are the black card.

Solution:-

(i) To find the probability of an Ace.

There are 4 ace in 52 cards. 1 ace in every suit.

So P(E) = 4/52 = 1/13

(ii) A red card

There are total 26 red cards. ( 13 cards of Hearts and 13 of Diamonds)

So, P(E) = 26/52 = 1/2

(iii) A face card

Face cards are Kings, Queens and Jacks.

So total face card is 12

So, P(E) = 12/52 = 3/13

(iv) A card of Heart

There are total 13 cards of Heart

So, P(E) = 13/52 = 1/4

(v) Neither King nor Queen

There are 4 kings and 4 Queen

So, total card = 52 - ( 4 + 4 ) = 44

So, P(E) = 44/52 = 11/13