What's the probability that my pants wear out today.

Question

I want to create a model for how pants are worn out.

I know that the expected life span of my pants is n days.

I don't know how old the pants are, and I don't have any way of measuring how worn they are. I am assuming that my pants will go from completely serviceable to completely worn out in a single day.

So, given only that the expected life span of my pants is n days, how do I figure out the probability that my pants will ware out on a given day?

Answer 1

Based on what you are assuming, the probability distribution should be "memoryless"; and according to wikipedia,

The only memoryless continuous probability distributions are the exponential distributions.

So you can obtain the desired probability using an exponential distribution with average $n$.