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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If A and B are mutually exclusive events, then

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