The … of armed robbery has been on the increase.

Analyze the question: The sentence is "The ____ of armed robbery has been on the increase." We need a noun that means the rate or frequency at which something occurs. This is a test of commonly confused words.

Explain the concept: Look at the four words:

• Accidence: the part of grammar dealing with word inflections (e.g., changes in word endings). It has nothing to do with crime.
• Accident: an unplanned event causing harm or damage. It doesn't fit, because armed robbery is deliberate, not accidental.
• Incident: a single event or occurrence (e.g., "a robbery incident"). It is a countable noun for one event, so it doesn't suit "has been on the increase" when speaking about armed robbery generally.
• Incidence: the extent, rate, or frequency of occurrence of something, especially something undesirable like crime or disease (e.g., "the incidence of malaria").

Show the solution:

1. The sentence talks about armed robbery increasing over time, which refers to how often it happens (its rate or frequency).
2. "Incidence" is the word for the rate of occurrence.
3. "The incidence of armed robbery has been on the increase" reads naturally. "Incident" would be used for a single event: "An incident of armed robbery occurred yesterday."

Answer: The correct option is D. incidence.

Tip: Remember that incidence = how often (rate), while incident = one event. If you can replace the word with "rate" or "frequency", choose incidence. Compare "the incidence of cholera" (how widespread it is) and "a cholera incident" (one case or event).