ProbabilityMCQMTP Nov 21Question 2803 of 295
All Questions

One card is drawn from a pack of 52, what is the probability that is a king or queen?

Options

A1113\displaystyle \frac{11}{13}
B213\displaystyle \frac{2}{13}
C113\displaystyle \frac{1}{13}
DNone of these
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Correct Answer

✅ Option b — 213\displaystyle \frac{2}{13}

All Options:

  • A1113\displaystyle \frac{11}{13}
  • B213\displaystyle \frac{2}{13}
  • C113\displaystyle \frac{1}{13}
  • DNone of these

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Detailed Solution & Explanation

Let K\displaystyle K represent the event of drawing a King and Q\displaystyle Q represent the event of drawing a Queen from a standard deck of 52 cards. 1. **Total number of cards** is n(Total)=52\displaystyle n(\text{Total}) = 52. 2. **Number of Kings** is n(K)=4\displaystyle n(K) = 4. 3. **Number of Queens** is n(Q)=4\displaystyle n(Q) = 4. Since a card cannot be both a King and a Queen, these two events are mutually exclusive, meaning K∩Q=∅\displaystyle K \cap Q = \emptyset and P(K∩Q)=0\displaystyle P(K \cap Q) = 0. Using the addition rule for mutually exclusive events: 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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