What is the difference between "incidence" and "occurrence"?

This was a question in a test: Do you have any figures showing the _______ of left-handedness in the general population?

Two of the answers were "occurrence" and "incidence". "incidence" was the answer, but I don't see why occurrence is not acceptable here.

EDIT: This was a language test, and only one answer was acceptable.

Solution 1:

Incidence refers to the rate of occurrence, not an instance of occurrence which is more close to incident as a synonym:

• The rate or extent of occurrence or effect: a high incidence of malaria in the tropics.

The following usage note may be helpful. : occurrence, happening, event, incident, episode

These nouns refer to something that takes place or comes to pass:

• Occurrence and happening are the most general: an everyday occurrence; a happening of no great importance. Event usually signifies a notable occurrence: world events reported on the evening news. "Great events make me quiet and calm; it is only trifles that irritate my nerves" (Victoria).
• Incident may apply to a minor occurrence: an incident that was blown out of proportion in the press. The term may also refer to a distinct event of sharp identity and significance: an incident that changed scientists' understanding of the phenomenon.
• An episode is an incident in the course of a progression or within a larger sequence: "Happiness was but the occasional episode in a general drama of pain" (Thomas Hardy).

The Free Dictionary

Solution 2:

The two words are generally synonymous in scientific usage. I am aware of a very slight difference, in that occurrence may mean the fact of something happening, as well as meaning the frequency of its occurrence. But such distinction is trivial, may not be agreed by other commentators, and does not justify saying that "occurrence" is an unacceptable answer. Unless the test related to a very specific course of study with clear and prior definition of terms, I feel the examiners were straining at subtleties that do not exist in general usage.