How likely is it that a computer miscalculates 1+1? Of course, normally a fully-functional computer will calculate 1+1=2. However, the physics governing the behavior of a chip is quantum mechanical. So in principle there is a certain probability that something goes wrong and we get the result 1+1=x where x≠2. In my opinion this probability should get bigger the smaller the chips are becoming.

So the question is: How likely is this event? Can one give an order of magnitude?

P.S. I'm not talking about quantum computing, just "standard" computers nowadays everyone has on their desk.
The probability of read error is bigger than write error, so there is a chance for bitflip on either of $1$ which might occur anywhere.
I can offer description of JVM attack which is not exactly the answer, but shows how much effort is needed to induce bitflips, tells about softerrors and a very successful attack on JVM, given good heat ;).

The probability of error grows the most related with heat dissipation problems, and making chip smaller include it's higher efficiency (performance per watt).

Anyway there is bad assumption - making chip smaller gives more errors - if this were true over time CPUs would generate noticeable amount of errors today.

Please check also this error rate study. With calculating probability of error there is a problem - this is hardware dependent and the most of hardware actually has errors, but they get corrected at several levels, so they do not occur for user, and with invalid / broken piece machine crashes are to often to perform test.