ProbabilityMCQMTP Dec 22 Series IIQuestion 2824 of 295
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A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of getting two kings:

Options

A752\displaystyle \frac{7}{52}
B1221\displaystyle \frac{1}{221}
C3221\displaystyle \frac{3}{221}
DNone of these
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Correct Answer

✅ Option b — 1221\displaystyle \frac{1}{221}

All Options:

  • A752\displaystyle \frac{7}{52}
  • B1221\displaystyle \frac{1}{221}
  • C3221\displaystyle \frac{3}{221}
  • DNone of these

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Detailed Solution & Explanation

We want to find the probability of drawing two Kings consecutively without replacement from a standard deck of 52 cards. 1. The probability that the first card drawn is a King is: P(K1)=452=113P(K_1) = \frac{4}{52} = \frac{1}{13} 2. Since the drawing is without replacement, there are now 51 cards remaining in the deck, including 3 Kings. 3. The conditional probability that the second card drawn is a King given that the first was a King is: P(K2/K1)=351=117P(K_2 / K_1) = \frac{3}{51} = \frac{1}{17} 4. The probability of getting both Kings is the product of these probabilities: P(K1∩K2)=P(K1)×P(K2/K1)=113×117=1221P(K_1 \cap K_2) = P(K_1) \times P(K_2 / K_1) = \frac{1}{13} \times \frac{1}{17} = \frac{1}{221} 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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