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Do Any Stars NOT Have Planets?

Astronomers have used a few different methods to detect exoplanets, and improved telescopes are increasing the rate of discovery. But is it possible that any stars DON’T have planets, or are they just an expected feature of stellar formation?

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Sources:

http://www.planetary.org/explore/space-topics/exoplanets/how-to-search-for-exoplanets.html
https://exoplanets.nasa.gov/interactable/11/
https://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html
https://www.nasa.gov/press-release/nasa-telescope-reveals-largest-batch-of-earth-size-habitable-zone-planets-around
http://www.space.com/30240-alien-planets-exoplanet-search-methods-infographic.html
http://curious.astro.cornell.edu/about-us/77-the-universe/extrasolar-planets/general-questions/323-how-are-planets-detected-around-other-stars-intermediate
https://exoplanets.nasa.gov/the-search-for-life/exoplanets-101/
http://www.space.com/24894-exoplanets-habitable-zone-red-dwarfs.html
http://home.strw.leidenuniv.nl/~keller/Teaching/ADA_2011/ADA_2011_L06_Exoplanets.pdf
https://arxiv.org/abs/1508.01338
http://iopscience.iop.org/article/10.1086/506930/pdf

Images:

https://commons.wikimedia.org/wiki/File:PIA21429_-_Transit_Illustration_of_TRAPPIST-1_(cropped).jpg
https://commons.wikimedia.org/wiki/File:ESO_-_The_Radial_Velocity_Method_(by).jpg
https://commons.wikimedia.org/wiki/File:HD189733b.jpg

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