# Multi-processing cpu utilization estimate

I find a formula on my book to estimate cpu utilization under multi-processing.

$U = 1 - P^n$

U: cpu utilization P: cpu idle

I want to know why or how to proof.

Edit:

The book is about operating system, not in english.

I get an answer that is

it's just basic probability theory

• What book? What are these variables? There is no proof afterwards? – Evil Jun 13 '18 at 11:03

$P^n$ is the probability that all "cores" are idle simultaneously, hence $1-P^n$ is the probability that at least one core is in use.
• why using $P^n$, not $nP$ or others? Just experienced? – Vonfry Jun 14 '18 at 1:09