Suppose there is a box of X keys and that each key is equall

Suppose there is a box of X keys and that each key is equally likely to open the lock. A guy then trys each key independently and at random. Let the variable N be the number of tries until the lock is opened.

What is the pmf of N if the unsucessful keys are put back in the box after being tried?

What is the pmf of N if the unsucessful keys are NOT put back in the box after being tried?

Solution

The pmf of N if the unsuccessful keys are put back in the box after being tried is Geometric distribution

the pmf of N if the unsucessful keys are NOT put back in the box after being tried is Negative binomial distribution.