GATE CSE 2022 | GA Question: 8

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?

• A. $\frac{1}{2}$
• B. $\frac{8}{25}$
• C. $\frac{19}{50}$
• D. $\frac{23}{50}$

Answer 1

Answer : Option D.

We can solve it using tree diagram.

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

Comments

@Sachin Mittal 1 Sir, in question its stated that “if an orange ball is drawn , it is replaced with another orange ball.”

so probability should be = $\frac{3}{5}*\frac{2}{4} + \frac{2}{5}*\frac{3}{6}=\frac{1}{2}$

correct me if I’m wrong.

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“ replaced with another orange ball “ – that doesn’t mean, add one more orange ball

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Tree Method is explained here, with many probability related questions solved using this simple method.

https://youtu.be/hvqk00SAoyk

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I think answer should be 1/2

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@Gyanu

here replacing with another orange ball means which  u draw ball it   replace the same size ball and colour  keep in the box

this is your big mistakes

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Are you going to challenge it bro i feel the same 1/2 as answer.

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@Chandrabhan Vishwa 1

Brother, Do you think both following sentences are same ?

(1) it is replaced with another orange ball.

(2) it is replaced with an orange ball.

 

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@Gyanu

yes  i think same 

key of the question is replace 

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@Gyanu

yes  i think same 

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We should challenge this question. In sentence “If a green ball is drawn, it is not replaced”, replacement meant putting the ball back in the box. So in the sentence “If an orange ball is drawn, it is replaced with another orange ball.” can be interpreted as “If an orange ball is drawn, it is put back in the box with another orange ball”.  ½ is also an option.

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@Gyanu did you challenged?

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https://gateoverflow.in/?qa=blob&qa_blobid=13009741460392416765

@Chandrabhan Vishwa 1   watch the above video clip , by Saurabh Thakur (  IIM passout, CAT faculty ) 

• Stackexchange Reference - 

https://math.stackexchange.com/questions/1695378/probability-third-draw-from-an-urn-having-black-and-white-balls

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Unfortunately the challenge was not accepted by IIT KGP  ( I will attach the document herewith )

This  is for all upcoming aspirants , as I have discussed this ques with many people ( from faculties , IIM passouts ) and what  I have gathered ,will keep it open .

” A orange ball is drawn with replacement ...”

A very standard sentence from the context of Probability 

What does it convey ?

• Draw a ball
• see the color 
• if its Orange , put the same ball back into the sack.

It does not mean -

A ball is drawn and if it's orange then it is replaced with another orange ball , if it is so , it SHOULD be mentioned whether it is replaced with a ball of same or different color .

The meaning of the sentence is very clear and can be found in many standard books . “ Replaced “ word is not used literally here . It means , you draw , you see , if orange you put back the same ball .

Now , lets come back to the actual GATE question .

“ If a orange ball is drawn , it is replaced with another orange ball ..”

So this statement can either be considered as very poorly framed or it is not supposed to be same as “with replacement “. The reason is very simple , “ another “ word makes the sentence very ambiguous .It means ( from “ with replacement “ problem ) , the same ball along with another orange ball is put back .

Many people have argued on the fact that the question clearly says “ the ball is replaced with another ball “ . Going by the literal meaning it will mean the same as per GATE has given the key but 

WHY aren’t we going by literal meaning for “ with replacement “ problem ( as discussed above ) ?

Our claim was not to make option A or option D correct . It is indeed ambiguous , we wanted marks for both the options . 

It costed me and as well as to many GATE 2022 aspirants .

Challenge Document  ( with all references and links ) : 

https://gateoverflow.in/?qa=blob&qa_blobid=12184540374439047831 

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ya bro it cost me hard too. i may not get direct addmission to top 5 iits by this question only. no conceptual error just ambigious language by the professor’s and even they have not checked i think as other branch many of question question answer key got change but not for cse.

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@ayushayush591 

this type of similar  problem  have come in previous year  question .

ans given according option D

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There's absolutely no ambiguity here. If other organizations frame poor questions it's not the job of GATE to correct them. If there's any standard book or resource where "replaced with another " has a different meaning please do share here. Not some videos on YouTube or quora link.

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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 )

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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.

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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.

Answer 2

https://www.toppr.com/ask/question/an-urn-contains-2-white-and-2-black-balls-a/

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..

Comments

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.

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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.

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@rsonx bro did you challenged?