ProbabilityMCQMTP Dec 22 - Series IQuestion 2823 of 295
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A candidate is selected for interview for 3\displaystyle 3 posts. For the first there are 3\displaystyle 3 candidates, for second there are 4\displaystyle 4 and for third there are 2\displaystyle 2. What are the chances of his getting at least one post?

Options

A34\displaystyle \frac{3}{4}
B23\displaystyle \frac{2}{3}
C110\displaystyle \frac{1}{10}
D1\displaystyle 1
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Correct Answer

✅ Option a — 34\displaystyle \frac{3}{4}

All Options:

  • A34\displaystyle \frac{3}{4}
  • B23\displaystyle \frac{2}{3}
  • C110\displaystyle \frac{1}{10}
  • D1\displaystyle 1

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Detailed Solution & Explanation

Let the candidate apply for three different posts. We assume that for each post, all candidates have an equal chance of being selected and the selection processes for the different posts are independent. 1. **For the first post:** There are 3 candidates. The probability that he gets selected is 13\displaystyle \frac{1}{3}. The probability that he does not get selected is: P(not selected for 1st)=1−13=23P(\text{not selected for 1st}) = 1 - \frac{1}{3} = \frac{2}{3} 2. **For the second post:** There are 4 candidates. The probability that he gets selected is 14\displaystyle \frac{1}{4}. The probability that he does not get selected is: P(not selected for 2nd)=1−14=34P(\text{not selected for 2nd}) = 1 - \frac{1}{4} = \frac{3}{4} 3. **For the third post:** There are 2 candidates. The probability that he gets selected is 12\displaystyle \frac{1}{2}. The probability that he does not get selected is: P(not selected for 3rd)=1−12=12P(\text{not selected for 3rd}) = 1 - \frac{1}{2} = \frac{1}{2} 4. The probability that he does not get selected for any of the posts is the product of his individual rejection probabilities: P(gets no post)=23×34×12=14P(\text{gets no post}) = \frac{2}{3} \times \frac{3}{4} \times \frac{1}{2} = \frac{1}{4} 5. The probability of getting at least one post is: P(gets at least one post)=1−P(gets no post)=1−14=34P(\text{gets at least one post}) = 1 - P(\text{gets no post}) = 1 - \frac{1}{4} = \frac{3}{4} 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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