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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § Chapter Opening and Epigraph § 14.1 Probability — A Theoretical Approach § 14.2 Summary
A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is :
  1. (a) $\dfrac{1}{13}$
  2. (b) $\dfrac{9}{13}$
  3. (c) $\dfrac{4}{13}$
  4. (d) $\dfrac{12}{13}$
Previously asked in CBSE board exam
2023 30/4/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer

(d) $\dfrac{12}{13}$

Total cards = 52; number of aces = 4; cards that are not aces = 48.
$$P(\text{not an ace}) = \frac{48}{52} = \frac{12}{13}$$

Source: Chapter 14, Example 4(ii)

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Explanation

The examiner expects you to recall that a deck has 4 aces, leaving 48 non-ace cards. Dividing 48 by 52 and simplifying gives $\frac{12}{13}$. You can also use the complement: $1 - \frac{1}{13} = \frac{12}{13}$. Either method is acceptable; just show the key step.

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