According to quantum mechanics, there is a non-zero probability that a particle, such as an electron, can quantum tunnel through a potential barrier, such as a sheet of paper. However, the probability of such an event occurring depends on various factors, including the thickness and nature of the barrier, as well as the energy of the particle.
In the case of a cup sitting on a sheet of paper, the electron(s) within the cup will generally be bound to the atoms or molecules making up the cup material. These bound electrons are typically in a lower energy state, known as the ground state, and are confined to the cup due to the potential barrier provided by the electromagnetic forces within the cup.
For an electron to tunnel through the paper barrier, it would need to possess sufficient energy to overcome the potential energy barrier and the thickness of the paper. However, electrons in the ground state of typical cup materials are unlikely to have enough energy to overcome such barriers under normal conditions.
Moreover, quantum tunneling probabilities decrease exponentially with increasing barrier width and height. The thickness of a sheet of paper is typically many orders of magnitude larger than the characteristic length scales associated with electron tunneling. As a result, the probability of an electron tunneling through a sheet of paper under normal conditions is extremely low.
Therefore, it is highly unlikely that a single electron from a cup would quantum tunnel through a sheet of paper over a period of 10 years in a typical environment. Quantum tunneling effects are typically observed in specific experimental setups involving specific conditions and materials where the probabilities are significantly enhanced or controlled.