GATE CS 2022 Set 1 — Question 8
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 ProbabilityProbability & StatisticsEngineering MathematicsElementary Statistics & ProbabilityQuantitative AptitudeGeneral Aptitude
Engineering Mathematics → Probability & Statistics → Conditional Probability
Last updated
Question
A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.First ball is drawn. What is the probability of getting an orange ball in the next draw?
Correct answer
(D) (23)/(50)
Solution
Let denote drawing a green ball and denote drawing an orange ball.
Initial state: 3 Green, 2 Orange. Total = 5.Case 1: First ball is Green ().
Probability .
Since green is not replaced, the box now has 2 Green, 2 Orange. Total = 4.
Probability of drawing Orange next () = .Case 2: First ball is Orange ().
Probability .
Since orange is replaced with another orange ball, the composition remains 3 Green, 2 Orange. Total = 5.
Probability of drawing Orange next () = .Total Probability of :
Initial state: 3 Green, 2 Orange. Total = 5.Case 1: First ball is Green ().
Probability .
Since green is not replaced, the box now has 2 Green, 2 Orange. Total = 4.
Probability of drawing Orange next () = .Case 2: First ball is Orange ().
Probability .
Since orange is replaced with another orange ball, the composition remains 3 Green, 2 Orange. Total = 5.
Probability of drawing Orange next () = .Total Probability of :
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 1 Q1The antonym of the word protagonist is ________.2026 Set 2 Q1Expedite, Hasten, Hurry, __________ Fill the blank by choosing a word with a meaning similar to…2026 Set 1 Q2The figure shows two 4-tile patterns. [figure] Either one or both of the patterns can be used any…2026 Set 2 Q2A black square PQRS has been cut into two parts. One part of it is shown in Panel I. Which one of…2026 Set 1 Q3Consider a knock-out women’s badminton singles tournament where there are no ties. The loser in…