Let's play a little LEGO game. According to the size and the shape of the Milky Way, one would need 67 billion cubes with a 5 light-years edge to fill its space. We exclude the central bulge-located cubes since the conditions inside it are not ideal for life evolving; what remains is an approximate 63 billion cubes that are equally spread along the disk and the spiral arms of the Milky Way. Keep in mind that the 5 ly edge represents the average distance from one solar system to another for this region.
Now, inside the examined area, there are 4.65 billion G-type stars that can (potentially) possess exoplanets. This gives an approximate 13.5 cubes for every G-type star like our Sun out there. Let's consider now that out of all the G stars, only 1 out of a million has a rocky exoplanet with water and such surface attributes to sustain life in whatever form it takes, from bacteria to E.T. So it becomes 13.5 x 1M = 13.5 million cubes.
Putting all of them together into a REALLY BIG CUBE, we would have an edge of around 1,190 ly. With Earth standing right in the center of our little cube, the radius to the extremity would be 600 ly away—fun fact: exactly where Kepler-22b stands as the biggest known and confirmed candidate of our search so far.
But wait, we need an approximate calculation for INTELLIGENT LIFE out of overall life. A, let's say, approximate 1/1,000 fraction from the possible life-sustaining G stars, so it would be 13.5 million cubes x 1,000 = 13.5 billion cubes. And the edge of the BIGGEST CUBE has just raised to 11,906 ly. To this, we add 50% (since if we go hunting, that would be the whole distance we would have to fill up to the center of the immediate proximity cubes), so it becomes an overwhelming 17,859 ly.
I am very sorry to declare it here, but THE STATISTICAL POSSIBILITY OF MEETING OR BEING MET BY ALIEN LIFE IS ZERO TO NONE SINCE V_MAX = C . Have a good night .
EDIT AND CLOSING . ACCORDING TO THE ABOVE STATISTICAL CALCULATION , IN THE GALAXY AT THIS VERY MOMENT IN TIME AT LEAST ANOTHER 4 DISTINCT CIVILIZATIONS EXIST TOGETHER WITH OUR OWN - TOO BAD WE WILL NEVER BE ABLE TO CONTACT THEM OR TO BE CONTACTED BY THEM .