ProbabilityMCQMTP Nov 18Question 3297 of 187
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The probability of A solving a problem is 712\displaystyle \frac{7}{12} odds against solving a problem

Options

A5:7\displaystyle 5:7
B4:7\displaystyle 4:7
C5:8\displaystyle 5:8
D4:5\displaystyle 4:5
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Correct Answer

✅ Option a — 5:7\displaystyle 5:7

All Options:

  • A5:7\displaystyle 5:7
  • B4:7\displaystyle 4:7
  • C5:8\displaystyle 5:8
  • D4:5\displaystyle 4:5

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Detailed Solution & Explanation

**Odds Against Solving the Problem** Given: P(A solves)=712\displaystyle P(A \text{ solves}) = \frac{7}{12} P(A does not solve)=1−712=512\displaystyle P(A \text{ does not solve}) = 1 - \frac{7}{12} = \frac{5}{12} **Odds against** = P(not solving) : P(solving) = 512:712=5:7\displaystyle \frac{5}{12} : \frac{7}{12} = 5:7 This matches **Option A** (5:7), not option D (4:5). By mathematical derivation: Odds against = 5:7\displaystyle 5:7. 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.

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