In a computer coding scenario, we have a list containing n items, and we are interested in

determining whether a specific object is in the list. With probability p$,$ the object is in

the list, and its position is uniformly distributed, meaning the object is equally likely $($with

probability $1/$n$)$ to be at position $1,2,...,$ n if it is present. With probability $1$ p the

object is not in the list.

The computer program searches the list sequentially, starting from the first item and

proceeding to the end. If the object is in the list, the program will find it and stop at the

corrsponding position. However, if the object is not in the list, the program will examine all

n items and stop at the last position. Find the expected number of items searched through

before the program stops