ProbabilityMTP June 2023 Series IIQuestion 2828 of 240

From a deck of $52$ cards, two cards are drawn at random. What is the probability that they are a king and a queen, if the cards are drawn one after the other without replacement?

Options

A$\frac{4}{52} \times \frac{4}{51}$

B$\frac{4}{52} \times \frac{4}{51} + \frac{4}{52} \times \frac{4}{51}$

C$\frac{2 \times 4 \times 3}{52 \times 51}$

D$\frac{4 \times 4}{52 \times 51}$

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Correct Answer

✅ Option b — $\frac{4}{52} \times \frac{4}{51} + \frac{4}{52} \times \frac{4}{51}$

All Options:

A$\frac{4}{52} \times \frac{4}{51}$
B$\frac{4}{52} \times \frac{4}{51} + \frac{4}{52} \times \frac{4}{51}$
C$\frac{2 \times 4 \times 3}{52 \times 51}$
D$\frac{4 \times 4}{52 \times 51}$

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.

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