in this problem if i put all the white balls in one box then probability of choosing the white is max ie 1 but i i do this then i am getting the wrong answer please help
don’t forget that there are N boxes as well… so he also has to select one box out of the n boxes. For your answer, the final probability will be 1/N, whereas for other arrangements, u have to apply bayes theorem
edit: applying bayes theorem, probability of selecting the box with all the white balls: 1/n, and probability of taking out a white ball from that box is 1. So the probability for the entire task is 1x(1/N), i.e. 1/N (this is explaination for the case you mentioned).
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@gvaibhav21 what do you mean by final probability will be 1/N can you please elaborate your answer what will be the answer for N=2
what you meant was that you will put all n white ball in one box, and distribute the black balls in other boxes, right? So for this case the probability of taking out a white ball in 1/N, for eg. 1/2 in case of N=2
@gvaibhav21 i think you are correct but that wont be the maximum probability so can you please tell what would be the maximum probability for N=2
the correct arrangement for 2 will be: 1 white ball in first box, and one white , two black balls in second box, so answer is: 1/2+(1/2)x(1/3) = .66666667
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i said your logic will give this answer… the correct logic is something else entirely 
read the edit as well as the above comment carefully
you’re welcome