ProbabilityMCQMTP Jun 24 Series IIQuestion 3370 of 187
All Questions

One Card is drawn from pack of 52\displaystyle 52, what is the probability that it is a king or a queen?

Options

A1/13\displaystyle 1/13
B2/13\displaystyle 2/13
C1/13\displaystyle 1/13
D1/4\displaystyle 1/4
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Correct Answer

✅ Option b — 2/13\displaystyle 2/13

All Options:

  • A1/13\displaystyle 1/13
  • B2/13\displaystyle 2/13
  • C1/13\displaystyle 1/13
  • D1/4\displaystyle 1/4

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Detailed Solution & Explanation

**Probability of Drawing a King or a Queen** Total cards in a standard deck = 52 Let K\displaystyle K be the event of drawing a King, and Q\displaystyle Q be the event of drawing a Queen. - n(K)=4\displaystyle n(K) = 4 - n(Q)=4\displaystyle n(Q) = 4 Since a card cannot be both a King and a Queen at the same time, the events K\displaystyle K and Q\displaystyle Q are mutually exclusive: P(K∩Q)=0P(K \cap Q) = 0 Using the Addition Theorem of Probability: P(K∪Q)=P(K)+P(Q)=452+452=852=213P(K \cup Q) = P(K) + P(Q) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13} 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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