ProbabilityMCQMTP May 19Question 2795 of 295

If a card is drawn at random from a pack of 52 cards, what is the chance of getting a Spade or an ace?

Options

\displaystyle \frac{4}{13}

\displaystyle \frac{5}{13}

\displaystyle 0.25

\displaystyle 0.20

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Correct Answer

✅ Option a — $\displaystyle \frac{4}{13}$

All Options:

A $\displaystyle \frac{4}{13}$
B $\displaystyle \frac{5}{13}$
C $\displaystyle 0.25$
D $\displaystyle 0.20$

Detailed Solution & Explanation

In a standard deck of 52 cards: - Total number of cards =

\displaystyle 52

- Number of Spade cards =

\displaystyle 13

- Number of Aces =

\displaystyle 4

- Number of cards that are both a Spade and an Ace (Ace of Spades) =

\displaystyle 1

Using the addition rule of probability:

P(\text{Spade} \cup \text{Ace}) = P(\text{Spade}) + P(\text{Ace}) - P(\text{Spade} \cap \text{Ace})

P(\text{Spade} \cup \text{Ace}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}

This corresponds to Option A. Hence, **Option A** 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.

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