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

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

In a pack of 52 cards, there are 4 queen cards and 13 heart cards 

Given : P(A) = \(\frac{4}{52}\), P(B) = \(\frac{13}{52}\)

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

The formula used : Probability = 

 = \(\frac{favourable\,number\,of\,outcomes}{Total\,no.of\,outcomes}\)

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) = \(\frac{13}{52}\) (as favourable number of outcomes = 13 and total number of outcomes = 52)

Probability that card drawn is both queen and heart = P(A and B)= 1 

(as there is one card which is both queen and heart i.e queen of hearts)

P(A or B) = \(\frac{4+13-1}{52}\) = \(\frac{16}{52}\) = \(\frac{4}{13}\)

P(A or B) = \(\frac{4}{13}\)

Probability of a card drawn is either a queen or heart = P(A or B) = \(\frac{4}{13}\)

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