Part IV The Equations
I realize this blog may be more mathematical and abstract than some people want to get into. In that case you can pass to the next and final chapter of this series.
You can skip this one if you don’t want to get into detail of the math involved.
There are 2 equations that have been introduced over the last 50 years to describe the possibilities of most of these goals. The Drake Equation and more recently the Seager equation.
The Drake Equation

N is the number of civilizations in our galaxy with which we might hope to be able to communicate
 R* is the average rate of star formation in our galaxy
 fp is the fraction of those stars that have planets
 ne is the average number of planets that can potentially support life per star that has planets
 fl is the fraction of the above that actually go on to develop life at some point
 fi is the fraction of the above that actually go on to develop intelligent life
 fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
 L is the length of time such civilizations release detectable signals into space
The Seager Equation:

N is the number of planets with detectable biosignature gases
Where:
 N_{*} is the number of stars within the sample
 F_{Q} is the fraction of quiet stars
 F_{HZ} is the fraction with rocky planets in the habitable zone
 F_{O} is the fraction of observable systems
 F_{L} is the fraction with life
 F_{S} is the fraction with detectable spectroscopic signatures
Corollaries to Drake Equation:
The Drake equation is actually missing a critical parameter which is

D is the effectiveness of our search
I also wish to define these additional quantities:

Ns is the number of stars in the region we are looking

Ll is the number of years that living things exist on a typical planet

Li is the number of years sentient creatures exist on a planet

Nc is the number of advanced civilizations we will detect in a region of space
Nc = R* x Fp x Ne x Fl x Fi x Fc x L x D
The additional variables we need to know to come up with an alternate version of Drake or Seager for a region of space and for different questions are as follows:

N* is the number of stars we will observe in our survey
N* = Ns x D
where Ns is the total number of stars and D is the percentage of the total we will look at comprehensively.
I assert as well:
Ns x D ~= R* x L
Therefore,
Ni = Ns x D x Fp x Ne x Fl x Fi x Fc
 Where Ni is the number of sentient species
Nl = Ns x D x Fp x Ne x Fl
 Where Nl is the number of planets with life
Nh = Ns x D x Fp x Ne
 Where Nh is the number of planets that may support life
REPHRASING THE GOALS
We now have all the material we need to consider the goals and possibilities of life.
In this series
Part I – Goals for our desire to understand and find extraterrestrial friends
Part II – how big is our search area?
Part III – what are the problems in finding life