To open a lock, a key is taken out from a collection of n keys at random. If the lock is not opend with this key, it is put back into the collection and another key is tried. The process is repeated again and again. If it is given that with only one key in the collection, the lock can be opend, then the probability that the lock will open in n trials, is

Options

A. `(1/n)^(n)`
B. `((n-1)/n)^(n)`
C. `1-((n-1)/n)^(n)`
D. None of these

Answer

C

Explanation

Required probability = 1-P (spend the lock in n trials )
` = 1 - ((n-1)/n)^(n)`