ProbabilityMCQMTP Nov 19Question 2796 of 295

If one card is drawn at random from a pack of playing cards; find the probability it is neither a hearts nor a club:

Options

\displaystyle \frac{1}{4}

\displaystyle \frac{1}{2}

\displaystyle \frac{1}{8}

DNone of these

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Correct Answer

✅ Option b — $\displaystyle \frac{1}{2}$

All Options:

A $\displaystyle \frac{1}{4}$
B $\displaystyle \frac{1}{2}$
C $\displaystyle \frac{1}{8}$
DNone of these

Detailed Solution & Explanation

A standard pack of playing cards has 52 cards consisting of 4 suits: Hearts, Clubs, Diamonds, and Spades, with 13 cards each. - Number of Heart cards =

\displaystyle 13

- Number of Club cards =

\displaystyle 13

If a card is drawn at random, the probability that it is 'neither a Heart nor a Club' means it must be either a Diamond or a Spade: - Favorable cards =

\displaystyle 13 \text{ (Diamonds)} + 13 \text{ (Spades)} = 26 \text{ cards}

- Probability =

\displaystyle \frac{26}{52} = \frac{1}{2}

. This corresponds to Option B. Hence, **Option B** 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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