What to take by default in probability: with replacement or without replacement? 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?
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.
If you are an Indian student... More specifically CBSE student... You are recommended to assume without replacement if not specified in the question.