A marble can be balanced on the edge of a bowl so that with a small push it could either (1) roll into the bowl and oscillate back and forth inside it or (2) roll off the bowl, land on the floor, and break. Is this balanced position a point of stable or unstable equilibrium?

The balanced position is a point of unstable equilibrium.
A particle at rest at a point will remain at rest. Furthermore, if the particle is displaced slightly in either direction, by applying a force, will tend to return it, and it will oscillate about the equilibrium point. This equilibrium point is called as stable equilibrium.
A particle at rest at a point will remain at rest. However, if the particle is displaced even the slightest distance from this point, the force will tend to push it farther from the equilibrium position. This equilibrium point is called unstable equilibrium
The marble can be balanced on the edge of a bowl. With a small push the marble roll into the bowl and oscillate back and forth inside it. So when you disturb by applying external force it cannot back into its stable position which is its original state. Therefore it is an unstable equilibrium.
In the second case, with a small push the marble could roll of the bowl, land on the floor, and break. Again in this case the marble cannot back into its stable position which is its original state. Thus it is also an unstable equilibrium.