GATE ME 2015 Set 3 — Question 10
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumConditional ProbabilityProbabilityEngineering Mathematics
Engineering Mathematics → Probability → Conditional Probability
Last updated
Question
A coin is tossed thrice. Let be the event that head occurs in each of the first two tosses. Let be the event that a tail occurs on the third toss. Let be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
Correct answer
(B) Y and Z are dependent
Solution
The sample space for three coin tosses is , so .
1.Event : Head in first two tosses , .
2.Event : Tail on third toss , .
3.Event : Two tails in three tosses , .
Check independence:- For and : , . Since , and are independent. (Statement A is false).
- For and : , . Since , and are dependent. (Statement B is true, Statement C is false).
- For and : , . Since , and are dependent. (Statement D is false).
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 ME 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 Q11Domain is bounded by curve , ordinate , and axis. The value of…2026 Set 1 Q12Let be a scalar function. Then, is2026 Set 1 Q13The order and degree of the following differential equation are and , respectively.…2026 Set 1 Q14Newton-Raphson method for solving algebraic equations is based on2026 Set 1 Q15The exact solution of is represented as . If represents…