ICSE Class 10 • 2024 • 3 Marks

Probability: Card Probability Without Replacement

Official examination question with verified M1/A1 mark scheme and step-by-step mathematical reasoning.

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 $= 52 - 8 = 44$. $P = \frac{44}{52} = \frac{11}{13}$.
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