How many stars were studied that came up empty and surveyed before less than 4,000 stars can be shown with exoplanets, I do not know.
The Kepler mission using the transit method , IIRC, attempted to survey 150,000 stars.
The probability of finding a transit is simply D/2a. Where "D" is the diameter of the star and "a" is the semi-major axis.
For the Earth-Sun, the probability is just under 0.5%. For M-type stars with close-orbiting planets, I think it can be as high as 20%. [That would make for an interesting graph.

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The no. of exoplanets by discovery method was easy to add to the program:
[Note: updated to give percentages and today's list of exoplanets.]
So my observation here. There are billions of stars in the MW, yet today we know < 3700 have exoplanets. The article title stated, "Does every star have planets?" My answer is no and the article is a easy to read and understand too.
The article did mention that the no. of exoplanets is about equal to the no. of stars. This isn't something new, but a lot more data is needed to tweak this estimate.