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From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of its being a king or a queen

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

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

Given : P(A) = \(\frac{4}{52}\), P(B) = \(\frac{4}{52}\)

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

The formula used : Probability = 

\(\frac{favourable\,number\,of\,outcomes}{total\,number\,of\,outcomes}\)

P(A or B) = P(A) + P(B) - P(A and B) 

P(A) = \(\frac{4}{52}\) (as favourable number of outcomes = 4 and total number of outcomes = 52) 

P(B) = \(\frac{4}{52}\) (as favourable number of outcomes = 4 and total number of outcomes = 52) 

Probability that card drawn is king or queen = P(A and B)= 0

(as a card cannot be both king and queen in the same time)

P(A or B) =   \(\frac{4}{52}+\frac{4}{52}\) – 0 

P(A or B) = \(\frac{4+4}{52}\) = \(\frac{8}{52}\) =   \(\frac{2}{13}\)

P(A or B) =  \(\frac{2}{13}\)

Probability of a card drawn is king or queen = P(A or B) =  \(\frac{2}{13}\)

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