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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?

1. $\frac{1}{2}$
2. $\frac{8}{25}$
3. $\frac{19}{50}$
4. $\frac{23}{50}$

We can solve it using tree diagram.

Tree Diagram is the best method to solve many Probability Questions.

The questions in ISC 2015 ,stack exchange and the GATE ques are almost identical . You can check the links and sir the video lecture is not a random one . It's from one of the top CAT faculty,IIM grad.

PS- The person who has answered in stack exchange has good mathematical background. ( 15k + points )

ya but GATE committe can give both option as correct as in other branches they do. even after challeging this question they ignored. more importantly i think this question was made for a trap because why would they given ½ as option means they tried question with both method and given option they are clear and assume that ‘replaced with’ is same as ‘replaced by’ so we can’t argue they might researched.

For a moment I misread ISC as ISI and was very curious.

The stack exchange person was trying to explain a poorly framed question. Nothing more to comment. @shubhajit are you going for a PhD in time wasting? Still haven't done any assignment question in goclassroom right?

I'm sure this question would have got 0 support for an answer change among IIT professors. And next time when challenging for answer key, one should use standard books -- I'm sure you cannot find one for this question.

i know this question created a lot of ambiguity but i suggest all of you to go to this link and see that EXTRA BALLS ARE ADDED..

Every year, at least one question has such interpretation ambiguity.

Now it depends entirely on the GATE committee whether they will be convinced that it indeed is Ambiguous Or it is Not.

Wait for official first answer key, and if your answer is Not the one given by GATE committee, challenge the question using "standard resources". If they will be convinced, they will provide marks for Option A,D both..

But there is NO way that marks will be given to all.
Yes it should be challenged. If amguious language they had given they should not give 1/2 as option.

@Deepakk Poonia (Dee)  sir , what do you think , is it worth challenging if GATE doesnt give ½ as ANS ?

Yes. It is worth challenging as it can affect your rank by a lot. Challenge the question using standard resources’ references. Stackoverflow, I guess, can also be used as a reference while challenging.

hi, we all should challenge this question together. If only few person challenges it then the gate committee would ignore the challenge. But if several people challenge it then they would consider it. I created a temporary discord server for discussing on challenging this question, please join https://discord.gg/wkdWj5J3Ja . 2 marks is a lot, don’t let it go.

@rsonx bro did you challenged?