ProbabilityMCQMTP Apr 21Question 2802 of 295
All Questions

A card is drawn from a pack of playing cards at random. What is the probability that the card drawn a king or red colour?

Options

A14\displaystyle \frac{1}{4}
B413\displaystyle \frac{4}{13}
C713\displaystyle \frac{7}{13}
D12\displaystyle \frac{1}{2}
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Correct Answer

✅ Option c — 713\displaystyle \frac{7}{13}

All Options:

  • A14\displaystyle \frac{1}{4}
  • B413\displaystyle \frac{4}{13}
  • C713\displaystyle \frac{7}{13}
  • D12\displaystyle \frac{1}{2}

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Detailed Solution & Explanation

Let K\displaystyle K represent the event of drawing a King and R\displaystyle R represent the event of drawing a red card from a standard deck of 52 cards. 1. **Total number of cards** in a standard pack is n(Total)=52\displaystyle n(\text{Total}) = 52. 2. **Number of Kings** in the deck is n(K)=4\displaystyle n(K) = 4. The probability of drawing a King is: P(K)=452P(K) = \frac{4}{52} 3. **Number of red cards** (Hearts and Diamonds) in the deck is n(R)=26\displaystyle n(R) = 26. The probability of drawing a red card is: P(R)=2652P(R) = \frac{26}{52} 4. **Number of red Kings** (King of Hearts and King of Diamonds) is n(K∩R)=2\displaystyle n(K \cap R) = 2. The probability of drawing a red King is: P(K∩R)=252P(K \cap R) = \frac{2}{52} Using the addition theorem of probability, the probability of drawing a King or a red card is: P(K∪R)=P(K)+P(R)−P(K∩R)P(K \cup R) = P(K) + P(R) - P(K \cap R) P(K∪R)=452+2652−252=2852=713P(K \cup R) = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} = \frac{28}{52} = \frac{7}{13} Hence, **Option C** 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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