Question

There are N + 1 identical boxes each containing N wall clocks. The r^th box contains (r – 1) defective and (N − r + 1) effective clocks for 1 ≤ r ≤ N + 1. A box is selected at random and from this box a clock is chosen at random and is found to be effective. The probability that it is from kth box is (2N - 2k + λ)/(N² + N), then find λ.

Answer 1

Probability of selection of any box is 1/(N + 1).

Let E be the event that the wall clock selected is effective. Then