Given $N$ boxes , $N$ white balls and $N$ black balls
chooses one box randomly and one ball from it randomly
Find the probability of getting white ball.
[Math] N white and black balls and N boxes Probability
probability
probability
Given $N$ boxes , $N$ white balls and $N$ black balls
chooses one box randomly and one ball from it randomly
Find the probability of getting white ball.
Best Answer
It depends on how the balls are distributed among the boxes. We will assume each box has at least one ball. Then we could put a white into $N-1$ of the boxes, and all $N$ black and the remaining white into the last box. The probability of white is then $\frac{N-1}{N}+\frac{1}{N(N+1)}$. This is close to $1$ if $N$ is large. Similarly, by an analogous distribution, we can make the probability of black close to $1$.
If on the other hand we put $2$ balls in each box by a process that does not pay attention to the colours of the balls, then by symmetry the answer is $1/2$.