GATE EE 2017 Set 2 — Question 1
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyConditional ProbabilityProbabilityEngineering Mathematics
Engineering Mathematics → Probability → Conditional Probability
Last updated
Question
An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
Correct answer
(A) (1)/(2)
Solution
Let and be the events that the first ball drawn is red and black respectively. and . Let be the event that the second ball drawn is red. By the law of total probability:If the first ball was red, 4 red and 5 black remain: .
If the first ball was black, 5 red and 4 black remain: .
Thus, .
Alternatively, by symmetry, since no information is revealed about the first draw, the probability of drawing a red ball on any subsequent draw remains the same as the initial probability.
If the first ball was black, 5 red and 4 black remain: .
Thus, .
Alternatively, by symmetry, since no information is revealed about the first draw, the probability of drawing a red ball on any subsequent draw remains the same as the initial probability.
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 EE 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 Q14Consider the following differential equation:…2026 Set 1 Q30Two matrices and have a common eigenvalue , and the same corresponding…2026 Set 1 Q32Given that , the integral…2026 Set 1 Q35 is an skew-symmetric matrix with real-valued entries, and is an…2026 Set 1 Q36A time-limited waveform is specified as follows:…