GATE EC 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 / -0.67MediumBayes' TheoremProbabilityEngineering MathematicsConditional Probability
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 be the double-headed coin (HH), be the double-tailed coin (TT), and be the fair coin (HT). The probability of selecting any coin is . Let be the event that the face showing after the toss is heads. We are looking for the probability that the other face is tails, which implies the coin selected must be the fair coin . Thus, we need to calculate the conditional probability .By Bayes' Theorem:The total probability of seeing a head
P(H) is calculated using the law of total probability:Now, substitute the values into the Bayes' formula:Alternatively, consider the total number of heads across all coins. There are 3 heads in total (2 from and 1 from ). If a head is observed, it is equally likely to be any of these 3 heads. Only 1 of these 3 heads (the one on ) has a tail on the other side. Thus, the probability 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 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.
Also appeared in
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 …