This is an interview question.
Given n red balls and m blue balls and some containers, how would you distribute those balls among the containers such that the probability of picking a red ball is maximized, assuming that the user randomly chooses a container and then randomly picks a ball from that.
suppose we have c containers, distribute n/c read balls to each c. If c == 1, put all of them together, it is n/(m+n)
If c == 2, put 1 red in c1 and all left red and all blue ones in c2 in this way , we have: 1/2 + 1/2 *(n-1) /(m+n-1) > 1/2 If c == 3, put a red in c1, put a red in c2, put left red and all blue in c3, we have: 1/3 + 1/3 + 1/3 * (n-2)/(m+n-2) > 2/3 If c == n, put a red in each of p -1, and all left red and blue in pth container, we have: ( Sum of (1/n) from 1 to n-1 ) + ( 1/n * 1/(m+1) ) (n-1)/n + 1/n * 1/(m+1) == 1 (almost)
As n is large, the (n-1)/n is very close to 1 so that we maximize the probability to get a red balls.
Any better ideas ?