Even though most gun deaths are suicide [1], your odds of killing yourself via suicide are still low. There's slightly less than 1% chance of your life ending via suicide. Taking away guns to stop suicides is a pretty big NNT.
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[1]
Accidental discharge: 591
Suicide by firearm: 19,990
Assault by firearm: 11,068
Unknown involving firearms: 248
The claim regarding suicide vs homicide is easy to confirm (https://en.wikipedia.org/wiki/Gun_violence_in_the_United_Sta...). It is not possible to predict every suicide, the best we can do is make an approximation using obvious risk factors like hospitalization for mental illness. There are millions of gun owners in the US, so yes the chance of a suicide is small.