ProbabilityMCQMTP June 2023 Series IIQuestion 3302 of 187
All Questions

If a card is drawn randomly from a deck, the probability of the card being neither a red card nor a face card?

Options

A513\displaystyle \frac{5}{13}
B617\displaystyle \frac{6}{17}
C1227\displaystyle \frac{12}{27}
D513\displaystyle \frac{5}{13}
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Correct Answer

✅ Option a — 513\displaystyle \frac{5}{13}

All Options:

  • A513\displaystyle \frac{5}{13}
  • B617\displaystyle \frac{6}{17}
  • C1227\displaystyle \frac{12}{27}
  • D513\displaystyle \frac{5}{13}

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Detailed Solution & Explanation

**Neither Red Nor Face Card** In a deck of 52 cards: - Red cards = 26 (Hearts + Diamonds) - Face cards = 12 (J, Q, K of each suit) - Red face cards = 6 (J, Q, K of Hearts + J, Q, K of Diamonds) Cards that are red OR face cards: ∣Red∪Face∣=26+12−6=32|\text{Red} \cup \text{Face}| = 26 + 12 - 6 = 32 Cards that are **neither red nor face**: 52−32=2052 - 32 = 20 These are black non-face cards (Ace, 2-10 of Spades and Clubs): - Spades: A,2,3,4,5,6,7,8,9,10 = 10 cards - Clubs: A,2,3,4,5,6,7,8,9,10 = 10 cards - Total = 20 P(neither red nor face)=2052=513P(\text{neither red nor face}) = \frac{20}{52} = \frac{5}{13} Hence, **Option A** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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