ProbabilityMCQMTP May 19 Series IIQuestion 2811 of 295
All Questions

If an unbiased die is rolled once, odds in favour of getting a point which is a multiple of 3 is

Options

A1:2
B2:1
C1:3
D3:1
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Correct Answer

✅ Option a — 1:2

All Options:

  • A1:2
  • B2:1
  • C1:3
  • D3:1

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Detailed Solution & Explanation

When an unbiased die is rolled once: 1. **Sample Space** is S={1,2,3,4,5,6}\displaystyle S = \{1, 2, 3, 4, 5, 6\}, so total outcomes n(S)=6\displaystyle n(S) = 6. 2. Let E\displaystyle E be the event of getting a multiple of 3. The multiples of 3 in the sample space are: E={3,6}E = \{3, 6\} So the number of favorable outcomes is n(E)=2\displaystyle n(E) = 2. 3. The remaining outcomes are non-multiples of 3: E′={1,2,4,5}E' = \{1, 2, 4, 5\} So the number of unfavorable outcomes is n(E′)=4\displaystyle n(E') = 4. 4. The **odds in favor** of event E\displaystyle E is defined as the ratio of the number of favorable outcomes to unfavorable outcomes: Odds in favor=n(E)n(E′)=24=12=1:2\text{Odds in favor} = \frac{n(E)}{n(E')} = \frac{2}{4} = \frac{1}{2} = 1:2 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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