Q. 12

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Answer :

let A denote the event that the card drawn is spade and B denote the event that card drawn is king.


In a pack of 52 cards, there are 13 spade cards and 4 king cards


Given : P(A) = , P(B) =


To find : Probability that card drawn is either a queen or heart = P(A or B)


The formula used : Probability =


P(A or B) = P(A) + P(B) - P(A and B)


P(A) = (as favourable number of outcomes = 13 and the total number of outcomes = 52)


P(B) = (as favourable number of outcomes = 4 and the total number of outcomes = 52)


The probability that card is drawn is both spade and king = P(A and B)= 1


(as there is one card which is both spade and king i.e. king of spades)


P(A or B) = + – 1


P(A or B) =


P(A or B)=


Probability of a card drawn is either a spade or king = P(A or B) =


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