GATE ME 2014 Set 1 — 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 MathematicsBayes' Theorem
Engineering Mathematics → Probability → Bayes' Theorem
Last updated
Question
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
Correct answer
(B) 1/3
Solution
Let the three coins be:
- : Two heads (HH)
- : Two tails (TT)
- : One head and one tail (HT)
- (since a coin is chosen at random)
- (the coin has two heads, so it must show a head)
- (the coin has two tails, so it cannot show a head)
- (the coin is fair, so it shows a head with probability 1/2)
P(H), is:Now, substitute these values into the Bayes' formula:Therefore, the probability that the other face is tails 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 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.
Also appeared in
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…