ProbabilityMCQMTP May 20Question 2798 of 295

What is the chance of picking a spade or an ace not of spade from a pack of 52 cards?

Options

\displaystyle \frac{4}{13}

\displaystyle \frac{2}{13}

\displaystyle \frac{3}{26}

\displaystyle \frac{3}{18}

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Correct Answer

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

All Options:

A $\displaystyle \frac{4}{13}$
B $\displaystyle \frac{2}{13}$
C $\displaystyle \frac{3}{26}$
D $\displaystyle \frac{3}{18}$

Detailed Solution & Explanation

In a standard deck of 52 cards: 1. There are 13 spades. 2. There are 4 aces, out of which 1 is the Ace of Spades. So, there are 3 aces that are not spades. 3. Since these two groups of cards ('spade' and 'ace not of spade') are mutually exclusive, the number of favorable cards is:

13 + 3 = 16 \text{ cards}

4. The probability of picking one of these cards is:

\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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