GATE CS 2015 Set 1 — Question 9
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumSample Space & EventsProbability & StatisticsEngineering Mathematics
Engineering Mathematics → Probability & Statistics → Sample Space & Events
Last updated
Question
The probabilities that a student passes in Mathematics, Physics and Chemistry are , , and respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in , , :
(I)
(II)
(III)
(I)
(II)
(III)
Correct answer
(D) Relations I and III are true.
Solution
Let , , and be the events of passing in Mathematics, Physics, and Chemistry, respectively. The probabilities are , , and .We are given the following probabilities:
We know that .
So, .We also know that .
So, .Now, let's evaluate the sum of individual probabilities, :
Now let's check the given relations:Relation (I):
. Since , Relation (I) is TRUE.Relation (II):
. Since , Relation (II) is FALSE.Relation (III):
In the context of such problems, often refers to the probability of passing all three subjects, i.e., . This is exactly .
We calculated .
Since , Relation (III) is TRUE (assuming represents ).Therefore, Relations I and III are true.The final answer is
1.
2.
3.
Let's define:We know that .
So, .We also know that .
So, .Now, let's evaluate the sum of individual probabilities, :
Now let's check the given relations:Relation (I):
. Since , Relation (I) is TRUE.Relation (II):
. Since , Relation (II) is FALSE.Relation (III):
In the context of such problems, often refers to the probability of passing all three subjects, i.e., . This is exactly .
We calculated .
Since , Relation (III) is TRUE (assuming represents ).Therefore, Relations I and III are true.The final answer is
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 CS 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 & Statistics
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…