GATE CS 2023 Set 1 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0MediumSample Space & EventsProbability & StatisticsEngineering MathematicsConditional Probability
Engineering Mathematics → Probability & Statistics → Conditional Probability
Last updated
Question
Consider a random experiment where two fair coins are tossed. Let be the event that denotes HEAD on both the throws, be the event that denotes HEAD on the first throw, and be the event that denotes HEAD on the second throw.
Which of the following statements is/are TRUE?
Which of the following statements is/are TRUE?
Correct answer
(C) B and C are independent.; (D) Prob(B C) = Prob(B)
Solution
The sample space for tossing two fair coins is . The total number of outcomes is 4.Define the events:
.
.
.
Since , and are not independent.Option (B): and
.
.
.
Since , and are not independent.Option (C): and
.
.
.
Since , and are independent.Option (D):
By definition of conditional probability, .
From above, and .
.
Since , the statement holds true. (This is also a direct property of independent events).Thus, options (C) and (D) are correct.
- : HEAD on both throws = . .
- : HEAD on first throw = . .
- : HEAD on second throw = . .
.
.
.
Since , and are not independent.Option (B): and
.
.
.
Since , and are not independent.Option (C): and
.
.
.
Since , and are independent.Option (D):
By definition of conditional probability, .
From above, and .
.
Since , the statement holds true. (This is also a direct property of independent events).Thus, options (C) and (D) are correct.
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…