The Drake equation (1961)  is an equation which tries to estimate the number of alien species who live in our galaxy Milky Way
For 2020 there is an updated version of this equation (the ACP) with a more accurate estimate of the number of planets that could support life.
The study: The Astrobiological Copernican principle →
A review of the study in Forbes magazine →
The Astrobiological Copernican principle
(Drake equation 2020)


Modelling scenario  
Number of stars (N*) ⌄Total number of stars in our galaxy  the Milky Way 
250 billion 
Mature stars (fL) ⌄The percentage of stars in our galaxy, which are older than 5 billion years 
1.5%
3.1%
96.3%

Habitable zone (fHZ) ⌄The percentage of stars in our galaxy, which have a planet that is old enough in the habitable zone 
19% 
Metallicity (fM) ⌄The percentage of stars in our galaxy, which have a high enough metal content for life and technology to exist 
49.83%
81.72%
97.38%

Available time (τ′) ⌄The average amount of time available for life to evolve on a planet 
1 bn yrs
2 bn yrs
4.8 bn yrs

Lifetime of signals (L) ⌄How long has the advanced civilisation being transmitting into space 
100 yrs

Results:


Number of Alien civilizations (N) ⌄
Estimated number of advanced civilisations in the Milky Way 
36
60
928

N = N* * fL * fHZ * fM * (L/τ')  
Estimated number of Earthlike planets in Milky Way 
355 million
1.2 billion
44 billion

Odds of intelligent life / planet 
1: 10 million
1: 490 million
1: 200 million

How do we apply the revisited Drake equation (2020) to the whole Universe?
We multiply the results from our galaxy Milky Way to 2 trillion galaxies (our latest estimate for the number of galaxies in the Universe as of 2020).
Even if this approach might seem simplistic, we are just trying to make an estimation of scale.
To apply the Drake equation to the whole Universe, could be a much more complicated affair with many other variables and estimations  and it is definitely something we hope scientists will look into someday.
Drake Model Optimistic  Drake Model Moderate  Drake Model Pessimistic  
Aliens in Our Galaxy  928  60  36 
Aliens in Universe 
1.8 quadrillion ⌄928 * 2 trillion galaxies 
120 trillion ⌄60 * 2 trillion galaxies 
72 trillion ⌄30 * 2 trillion galaxies 
1.8 quadrillion alien civilizations in Universe?
Isn't that a bit too much?
Those huge numbers could be because the scientists in the study assumed that life always appears on Earthlike planets within a few billion years as a natural part of evolution (mathematically, chances are assumed to be 1:1  life always appears).
What if life is rarer than they believe?
Another study →
that is using bayesian statistics found that chances of life appearing could be 9:1 for primordial life and 3:2 for intelligent life.
Chances for Intelligent Life  Drake Model Optimistic  Drake Model Moderate  Drake Model Pessimistic 
1:1 (Drake 2020)  1.8 quadrillion  120 trillion  72 trillion 
3:2 (bayesian study *)  1 quadrillion  64 trillion  38 trillion 
1:million  1.8 billion  120 millions  72 millions 
1:billion  1.8 million  120 thousands  72 thousand 
However, what if we assume some aliens actually did not die as assumed in the latest 2020 Drake equation?
After all, why assume they died after 100 years? Maybe they just evolved away from using the radio.
How do we calculate how many aliens ever appeared?
For the 1:1 chances  that means that life always appears on a planet like Earth. So basically we only need to find the number of planets in the Universe. To find this, we have the stars in Universe (1×10^{24}) and then use the latest Drake equation (ACP) and take the worst scenario from there which gives us:
1×10^{24} (stars in Universe)
* 0.19 (% Stars with Earthlike planets  this is constant in ACP)
* 0.015 (Matured stars at least 5bn y old  this is the fL from the pessimistic scenario from ACP)
* 0.4983 (Metalicity  fM from the pessimistic scenario from ACP)
= 1.4E21 (1.4 sextillion Earthlike planets in Universe which could support life according with the most pessimistic scenario of the latest Drake equation)
Chances for Intelligent Life  Aliens who now have the same technological level as us  Some Survived (1%)  All aliens who ever appeared 
1:1 (Drake 2020)  72 trillion  14 quintillion (1.4E19)  1.4 sextillion (1.4E21) 
3:2 (bayesian study *)  38 trillion  75 quadrillion (756E16)  756 quintillion (756E18) 
1:million  72 millions  14 trillions  1.4 quadrillion (1.4E15) 
1:billion  72 thousands  14 billion  1.4 trillion (1.4E12) 
1:trillion  72  14 million  1.4 billion (1.4E9) 
The Fermi paradox, is the apparent contradiction between the lack of evidence for extraterrestrial civilizations and the high estimates for their probability
There are a lot of explanations for this apparent paradox among which:
Civilizations broadcast detectable radio signals only for a brief period of time
or
Earth is deliberately not contacted,
which look reasonable.
For example:
In a 2006 Sky & Telescope article, Seth Shostak wrote, "Moreover, radio leakage from a planet is only likely to get weaker as a civilization advances and its communications technology gets better. Earth itself is increasingly switching from broadcasts to leakagefree cables and fiber optics, and from primitive but obvious carrierwave broadcasts to subtler, hardtorecognize spreadspectrum transmissions."
Our galaxy  250 billion stars
Universe  2 trillion galaxies (2×10^{12})
Universe stars  1×10^{24}  more stars than all the grains of sand on planet Earth