ProbabilityMCQMTP Oct 21Question 2807 of 295
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Following are the wages of 8 workers in rupees: 50, 62, 40, 70, 45, 56, 32, 45. If one of the workers is selected at random, what is the probability that his wage would be lower than the average wage?

Options

A0.625\displaystyle 0.625
B0.500\displaystyle 0.500
C0.375\displaystyle 0.375
D0.450\displaystyle 0.450
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Correct Answer

✅ Option b — 0.500\displaystyle 0.500

All Options:

  • A0.625\displaystyle 0.625
  • B0.500\displaystyle 0.500
  • C0.375\displaystyle 0.375
  • D0.450\displaystyle 0.450

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Detailed Solution & Explanation

Let the wages of the 8 workers be: 50,62,40,70,45,56,32,45\displaystyle 50, 62, 40, 70, 45, 56, 32, 45. 1. **Find the average wage:** Average=50+62+40+70+45+56+32+458=4008=50\text{Average} = \frac{50 + 62 + 40 + 70 + 45 + 56 + 32 + 45}{8} = \frac{400}{8} = 50 2. **Identify wages lower than the average wage of 50:** - 40\displaystyle 40 - 45\displaystyle 45 - 32\displaystyle 32 - 45\displaystyle 45 These are 4 wages. Note that 50 is equal to the average, not lower than it. 3. **Number of favorable outcomes** is 4, and the **total number of workers** is 8. 4. **Probability** of selecting a worker whose wage is lower than the average wage is: Probability=48=0.500\text{Probability} = \frac{4}{8} = 0.500 Hence, **Option B** 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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