Only some times, generally it depends how massive the star is when it explodes.
If its less than about 8 solar masses (8 x the mass of the sun) then it probably won’t become a black hole. Towards the end of its life a star tends to loose a lot of material, so it decreases in mass, so even big stars can fall below the limit.
After it goes supernova – and it has to be a biggish star to do that, our own sun won’t for instance, then it depends how much is left over after the explosion.
If there is just a small amount, say about the mass of the sun, it will form a white dwarf. If its up to about 3 solar masses it will make a neutron star, and above that probably a black hole, although we don’t know precisely the exact mass required.
So – really it all depends how big it was to start with, and how much it lost before and during the time when it went bang!
As Julian says, only if the star was very large to begin with. Our Sun definitely won’t form a black hole. Some black holes aren’t formed from stars at all – for example the super massive black holes at the centre of galaxies.
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