GATE EC 2015 Set 2 — Question 5
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyElementary Statistics & ProbabilityQuantitative AptitudeGeneral AptitudeDefinitions of ProbabilityProbabilityEngineering Mathematics
Engineering Mathematics → Probability → Definitions of Probability
Last updated
Question
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is and that of Ramesh is . What is the probability that only one of them will be selected?
Correct answer
(B) 1/4
Solution
Let
Given:
The probability that only one of them is selected is the sum of the probabilities of two mutually exclusive events: (Ram is selected AND Ramesh is not) OR (Ram is not selected AND Ramesh is selected).
Since the selections are independent events:
.
P(A) be the probability that Ram is selected and P(B) be the probability that Ramesh is selected.Given:
The probability that only one of them is selected is the sum of the probabilities of two mutually exclusive events: (Ram is selected AND Ramesh is not) OR (Ram is not selected AND Ramesh is selected).
Since the selections are independent events:
.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Probability
2026 Set 1 Q1Among the following options, the antonym of the word ‘nocturnal’ is _________.2026 Set 1 Q2The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The…2026 Set 1 Q3The figure below has exactly three intersecting line segments with a rectangular portion …2026 Set 1 Q4Real numbers , , and (all greater than 1) satisfy…2026 Set 1 Q5The following observation is made about the scores obtained by 100 students in an exam: 'For each…