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Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

My approach towards the answer is:

I will find the total number of cases: selecting 2 balls out of (2+3+2).

I will find total number of cases which have no blue: selecting 2 balls out of (2 red + 3 green).

Here my question is: in the question no information is given for the replacement.

So what should I take it as: with replacement or without replacement?

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    $\begingroup$ implicitly I would say without replacement by the comment "drawn", but I'd also say "Ask the teacher what they meant by this" when the language is unclear $\endgroup$ – Alan Oct 12 '14 at 18:20
  • $\begingroup$ @Alan : so there is nothing so called "by Default" in case of probability. $\endgroup$ – munjal007 Oct 12 '14 at 18:27
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    $\begingroup$ My inclination would occur to say "default" would be without replacement, but that's a dangerous inclination. Never hurts to double check with the question poser. $\endgroup$ – Alan Oct 12 '14 at 18:28
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Let us assume the above question appears on an exam and the professor has a rule: no questions answered during the exam. How to best interpret the problem as given?

Question : A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

We are told that two balls are drawn at random. Since we are not told that the balls were returned to the bag, the simplest interpretation would be that the balls were drawn without replacement and should thus be solved accordingly.

If the instructor then came back and said, "i meant with replacement," then i as a professor of statistics for almost 30 years would say that the question was poorly worded and the student must get the benefit of the doubt. If the instructor did not intentionally set out to trick the student, then the instructor would agree. If the instructor did intend to trick the student, then i would find another instructor.

i hope this reply helps, best.

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  • $\begingroup$ so your interpretation is , if the no evidence of "putting the ball back" is given then we should take it as without replacement, that means by default "without replacement". $\endgroup$ – munjal007 Oct 15 '14 at 14:02
  • $\begingroup$ @munjal007 yes, though as suggested above "by default" is not a term generally used in statistics. A clearly and concisely worded question or statement in statistics should not, however, leave any doubt in the mind of the reader. Hence, unless "with replacement" or "the balls are put back in the urn" is clearly stated, any reasonable statistician would assume without replacement. $\endgroup$ – drphil Oct 16 '14 at 5:32
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If you are an Indian student... More specifically CBSE student... You are recommended to assume without replacement if not specified in the question.

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