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) = \(\frac{4}{13}\)