The probability of transmission, or the fraction of particles going through, depends on the width and height of the barrier. If you do the mathematics, you find that the probability decreases exponentially with increasing width and height of the barrier. This effect is called the tunnel effect . In classical terms this means that if you try to leave a room, you could attempt to tunnel through the wall. The time needed, however, turns out to be very large, much larger than the lifetime of the universe.
Small particles tunnel all the time, though.
Alpha decay of radio-active nuclei can be explained this way. An alpha particle is a He nucleus consisting of two protons and two neutrons. This is a very stable grouping. If one thinks about neutrons and protons moving in a nucleus, they tend to move in such groups of four. So we can think of a nucleus as a bunch of alpha particles moving around in a small region.