GATE EC 2014 Set 3 — Question 38
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumExpectation & VarianceProbabilityEngineering Mathematics
Engineering Mathematics → Probability → Expectation & Variance
Last updated
Question
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ______ .
Correct answer
2.9 to 3.1
Solution
Let be the random variable representing the number of tosses required until both a head (H) and a tail (T) have appeared at least once.
The first toss will result in either H or T. Suppose the first toss is H. Then we continue tossing until we get the first T. The number of additional tosses required to get the first T follows a geometric distribution with probability of success . The expected value of a geometric distribution starting from the first trial is .
Thus, the total expected number of tosses is .
By symmetry, if the first toss was T, the expected number of additional tosses to get the first H is also 2, leading to a total of 3 tosses.
Therefore, .
The first toss will result in either H or T. Suppose the first toss is H. Then we continue tossing until we get the first T. The number of additional tosses required to get the first T follows a geometric distribution with probability of success . The expected value of a geometric distribution starting from the first trial is .
Thus, the total expected number of tosses is .
By symmetry, if the first toss was T, the expected number of additional tosses to get the first H is also 2, leading to a total of 3 tosses.
Therefore, .
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.
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 …