GATE EC 2017 Set 2 — Question 29
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0EasyExpectation & VarianceProbabilityEngineering Mathematics
Engineering Mathematics → Probability → Expectation & Variance
Last updated
Question
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is ___________
Correct answer
2.4 to 2.6
Solution
This problem can be modeled using a geometric distribution. Let be the probability of success (getting a reservation) in a single attempt. Given . The random variable represents the number of attempts until the first success. For a geometric distribution where is the number of trials until the first success, the expected value (average number of attempts) is given by:Substituting the given probability:Thus, the average number of attempts that passengers need to make to get a seat reserved is 2.5.
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 Q11Consider the differential equation , with…2026 Set 1 Q12A surface is given by and and are unit…2026 Set 1 Q23The relation between the input current () and the output voltage () of a circuit is governed…2026 Set 1 Q26Consider the matrix . Which…2026 Set 1 Q36Consider the two series, and , where …