Q1. [1] § Chapter Opening and Epigraph § 14.1 Probability — A Theoretical Approach
A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is:
- A $\dfrac{3}{26}$
- B $\dfrac{3}{13}$
- C $\dfrac{2}{13}$
- D $\dfrac{1}{2}$
Previously asked in CBSE board exam
2025 30/1/1 Q13
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
Option A: $\dfrac{3}{26}$
A deck has 52 cards. Red face cards = kings, queens, jacks of hearts and diamonds = 6 cards.
$$P(\text{red face card}) = \frac{6}{52} = \frac{3}{26}$$
Source: Chapter 14, Section 14.1
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Explanation
- Face cards are kings, queens, and jacks only (3 per suit).
- Red suits are hearts and diamonds → 3 × 2 = 6 red face cards.
- Many students mistakenly count only one red suit or forget to simplify. Always simplify the fraction: 6/52 = 3/26.
- Option B (3/13 = 6/26) is double the correct answer — a common error from counting all 4 suits' face cards instead of only the 2 red ones.
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