Probability of choosing a number k uniformly at random from {1,…,N−1} = $\frac{1}{N-1}$
Number of way to choose k beads from N white beads = $\binom{N}{k}$
Number of way in which k black beads can occur sequentially in the circle = N
Required Probability = $\frac{1}{N-1}*\frac{N}{\binom{N}{1}} + \frac{1}{N-1}*\frac{N}{\binom{N}{2}} + .... + \frac{1}{N-1}*\frac{N}{\binom{N}{N-1}}$
= $\frac{N}{N-1}\sum_{k = 1}^{N - 1}\frac{1}{\binom{N}{k}}$
Answer : C