A card is drawn at random from well shuffled pack of 52 cards. Find the probability that the card drawn is : (i) a spade (ii) not of diamond

9. A card is drawn at random from well shuffled pack of 52 cards. Find the probability that the card drawn is :

(i) a spade

(ii) not of diamond

Sol. There are 52 cards in a pack

 ∴  n (S) = 52

(i) Let A be event that the card drawn is a spade card

∴  There are 13 spade cards

∴  n (A) = 13

P (A) = n (A)/n (S)

∴  P (A) = 13/52

∴  P (A) = ¼

(ii) Let B be event that the card drawn is not a diamond

There are 13 diamond cards

∴  There are 39 cards which are not of diamond

∴  n (B) = 39

P (B) = n (B)/n (S)

∴  P (B) = 39/52

∴  P (B) = 3/4