Quantum uncertainty affecting classical object? [duplicate]

As far as I know, the probability of a quantum object being in a certain position depends on the wave function value for each position. That raises a question: Is this probability strictly greater than 0 for all points? If I place an electron in a box, it can be anywhere on the box, or anywhere on the universe?

For example, there is always a small possibility of finding a value however far from the mean, while that is not the case for a triangular distribution.

Also, slightly related: Is this property maintained when studying classical objects? Is there any possibility, even if unimaginably small, that all of the particles of a cat will simply move somewhere else at the same time, "teleporting" it?

marked as duplicate by sammy gerbil, Jon Custer, stafusa, Qmechanic♦ quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Oct 31 '17 at 22:36

If the value of $|\psi|^2$ is greater than zero there is a probability of detecting the particle. Whether this is the case depends on the potential. For example if the particle is in an infinite potential well then $\psi$ is zero outside the box and there is no probability of detecting the particle outside the box. If the box is not an infinitely deep potential well then there is a probability of detecting the particle outside the box, though this probability rapidly falls to such small values that it is indistinguishable from zero.