GATE CS 2024 Set 1 — Question 63
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0EasyConditional ProbabilityProbability & StatisticsEngineering Mathematics
Engineering Mathematics → Probability & Statistics → Conditional Probability
Last updated
Question
A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is _________
Correct answer
0.37 to 0.38
Solution
Total number of red balls = 10
Total number of blue balls = 15
Total number of balls = 10 + 15 = 25Let be the event that the first ball drawn is red, and be the event that the second ball drawn is red.
The question asks for the probability that both balls are red given that the first ball is red. This is expressed as the conditional probability .By the definition of conditional probability:Using the multiplication rule, . Substituting this back:Since the balls are drawn without replacement, if the first ball is red, there are red balls remaining out of a total of balls.Thus, the probability is 0.375.
Total number of blue balls = 15
Total number of balls = 10 + 15 = 25Let be the event that the first ball drawn is red, and be the event that the second ball drawn is red.
The question asks for the probability that both balls are red given that the first ball is red. This is expressed as the conditional probability .By the definition of conditional probability:Using the multiplication rule, . Substituting this back:Since the balls are drawn without replacement, if the first ball is red, there are red balls remaining out of a total of balls.Thus, the probability is 0.375.
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…