ProbabilityMCQMTP June 22Question 3356 of 187
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A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 3/5\displaystyle 3/5 and that of wife's selection is 1/5\displaystyle 1/5. Then the probability that only one of them is selected is

Options

A16/25\displaystyle 16/25
B17/25\displaystyle 17/25
C14/25\displaystyle 14/25
DNone of these
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Correct Answer

✅ Option c — 14/25\displaystyle 14/25

All Options:

  • A16/25\displaystyle 16/25
  • B17/25\displaystyle 17/25
  • C14/25\displaystyle 14/25
  • DNone of these

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Detailed Solution & Explanation

**Probability That Only One of Them is Selected** Let H\displaystyle H and W\displaystyle W be the events that the husband and wife are selected, respectively. Given: - P(H)=35⇒P(Hˉ)=1−35=25\displaystyle P(H) = \frac{3}{5} \Rightarrow P(\bar{H}) = 1 - \frac{3}{5} = \frac{2}{5} - P(W)=15⇒P(Wˉ)=1−15=45\displaystyle P(W) = \frac{1}{5} \Rightarrow P(\bar{W}) = 1 - \frac{1}{5} = \frac{4}{5} Assuming the selection of husband and wife are independent events, the probability that only one of them is selected is: P(only one)=P(H)P(Wˉ)+P(Hˉ)P(W)P(\text{only one}) = P(H)P(\bar{W}) + P(\bar{H})P(W) P(only one)=(35×45)+(25×15)P(\text{only one}) = \left(\frac{3}{5} \times \frac{4}{5}\right) + \left(\frac{2}{5} \times \frac{1}{5}\right) P(only one)=1225+225=1425P(\text{only one}) = \frac{12}{25} + \frac{2}{25} = \frac{14}{25} Hence, **Option C** 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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