All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is (i) a red card, (ii) a face card, (iii) a card of clubs.
There are 6 red face cards which are removed.
Thus, remaining number of card = 52 – 6 = 46.
Total numbers of elementary events are: 46
(i) Let E be the event of getting a red card
Number of favourable outcomes now = 26 – 6 = 20.
∴ P (getting a red card) = P (E)= 20/46 = 10/23
(ii) Let E be the elementary event of getting a face card
Number of face cards now = 12 – 6 = 6.
Number of favourable events = 6
∴ P (getting a face card) = P (E) = 6/46 = 3/23.
(iii) Let E be the event of getting a card of clubs
The number of card of clubs = number of favourable event = 12.
∴ P (getting a card of clubs) = P (E) = 12/46 = 6/23