Q. To open a lock, a key is taken out from a collection of $n$ keys at random. If the lock is not opened 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 opened, then the probability that the lock will open in $n$ trials, is
A) $\left( \frac{1}{n} \right)^{n}$
B) $\left( \frac{n - 1}{n} \right)^{n}$
C) ${1 - \left( \frac{n - 1}{n} \right)}^{n}$
D) None of these
Explanation
(c)
Required probability
$= 1 - P$(not opened the lock in $n$ trials)
$= 1 - \left( \frac{n - 1}{n} \right)^{n}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.