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) = \(\frac{13}{52}\), P(B) = \(\frac{4}{52}\)
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) = \(\frac{13}{52}\) (as favourable number of outcomes = 13 and the total number of outcomes = 52)
P(B) = \(\frac{4}{52}\) (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) = \(\frac{13}{52}+\frac{4}{52}\) – 1
P(A or B) = \(\frac{13+4-1}{52}\) = \(\frac{16}{52}\) = \(\frac{4}{13}\)
P(A or B)= \(\frac{4}{13}\)
Probability of a card drawn is either a spade or king = P(A or B) = \(\frac{4}{13}\)
