ProbabilityMCQPYQ June 24Question 2810 of 295
All Questions

From a bag containing 4 red, 5 blue and 6 white caps, two caps are drawn without replacement. What is the probability that the caps are of different colours?

Options

A74105\displaystyle \frac{74}{105}
B37105\displaystyle \frac{37}{105}
C94105\displaystyle \frac{94}{105}
D31105\displaystyle \frac{31}{105}
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 74105\displaystyle \frac{74}{105}

All Options:

  • A74105\displaystyle \frac{74}{105}
  • B37105\displaystyle \frac{37}{105}
  • C94105\displaystyle \frac{94}{105}
  • D31105\displaystyle \frac{31}{105}

Ad

Detailed Solution & Explanation

Let the bag contain: - Red caps: 4\displaystyle 4 - Blue caps: 5\displaystyle 5 - White caps: 6\displaystyle 6 - Total caps: 4+5+6=15\displaystyle 4 + 5 + 6 = 15 Two caps are drawn at random without replacement. 1. **Total number of ways** to choose 2 caps from 15 is: (152)=15×142=105\binom{15}{2} = \frac{15 \times 14}{2} = 105 2. Let's find the probability of the complementary event (drawing two caps of the **same color**): - **Both Red:** (42)=4×32=6\displaystyle \binom{4}{2} = \frac{4 \times 3}{2} = 6 ways - **Both Blue:** (52)=5×42=10\displaystyle \binom{5}{2} = \frac{5 \times 4}{2} = 10 ways - **Both White:** (62)=6×52=15\displaystyle \binom{6}{2} = \frac{6 \times 5}{2} = 15 ways Total ways to draw two caps of the same color is: 6+10+15=31 ways6 + 10 + 15 = 31\text{ ways} 3. The probability of drawing two caps of the same color is: P(Same Color)=31105P(\text{Same Color}) = \frac{31}{105} 4. The probability of drawing two caps of different colors is: P(Different Colors)=1−P(Same Color)=1−31105=74105P(\text{Different Colors}) = 1 - P(\text{Same Color}) = 1 - \frac{31}{105} = \frac{74}{105} 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.

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.

More Questions from Probability

Mode can be obtained from________

The modes of presentation of data are:

The distribution of income is an example of frequency distribution of

In a frequency distribution, the relative frequency of the class is:

Histogram can be drawn when

Less than ‘o’give curve give

Ready to Master Probability?

Practice all 295 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free