Problem Statement
A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability that the card drawn is:
(i) A black face card.
(ii) A spade or an ace.
(iii) Neither a king nor a queen.
Verified Solution & Marking Scheme
Black Face Cards
Black suits: Spades and Clubs. Each has 3 face cards (J, Q, K). Total $= 6$. $P = \frac{6}{52} = \frac{3}{26}$.
Spade or Ace
13 spades + 3 other aces $= 16$ cards. $P = \frac{16}{52} = \frac{4}{13}$.
Neither King nor Queen
Kings (4) + Queens (4) $= 8$. Remaining cards $= 52 - 8 = 44$. $P = \frac{44}{52} = \frac{11}{13}$.