There are billions of galaxies, each with billions of stars, around each stars there may be planets which may have existed for billions of years. It seems that chance may have jumped through billions of hoops to leave us alone in the Universe. To find how many billions we need to do some calculations.
There are an estimated 50 billion galaxies are visible with modern telescopes and the total number in the universe must surely exceed this number by a huge factor, but we will ignore this and just take the 50,000,000,000 or so galaxies we can see.
The number of stars in an average galaxy may be hundreds of billions.
Lets call it just 100 billion.
So the total number of stars in the universe is roughly 50 billion x 100 billion.
That's 5,000,000,000,000,000,000,000 stars, 5 thousand, billion, billion. Properly known as 5 sextillion. That is still a conservative estimate.
We need to estimate how many stars have planetary systems. The original extra-solar system planet hunting technology dictated that a star needed to be to close to us for a planet to be detected, usually by the stars 'wobble'. Better technology that allows us to measure the dimming of a stars brightness when a planet crosses its disk has now revolutionised planet hunting and new planets are being discovered at an ever increasing rate. Even so, most cosmologists believe that planetary formation around a star is quite common place. For the sake of argument let us say it's not and rate it at only one in a million and only one planet in each system, as we want a conservative estimate, not an exaggerated one. That calculation results in 5,000,000,000,000,000 planets in the universe. Five million, billion, as a conservative estimate.
And now we must estimate the number of planets capable of supporting life. Let's assume that this is very rare among planets and rate it at only one in a million. Simple division results in:
5,000,000,000 planets in the universe capable of producing life. Ten billion!
We have been sending out radio signals into the Universe since early in the Twentieth Century. Those signals have now reached a distance maybe 100 light years from us. There are hundreds of planets within a hundred light years distance from us. If there is intelligent life on any of those planets, with their own radio technology, capable of separating those signals out from all the other radio signals from all the many sources in the Universe, they may already know of our existence. They may have known for decades.
The same thing is happening in reverse. The SETI project is analysing radio signals from the Universe for any signal of extra terrestrial life. Nothing has been found yet.