Binomial or Poisson?

I found the following handy tip on Jonathan Deane's site (University of Surrey):

• If a mean or average probability of an event happening per unit time/per page/per mile cycled etc., is given, and you are asked to calculate a probability of n events happening in a given time/number of pages/number of miles cycled, then the Poisson Distribution is used.
• If, on the other hand, an exact probability of an event happening is given, or implied, in the question, and you are asked to caclulate the probability of this event happening k times out of n, then the Binomial Distribution must be used.

He also has some sample problems on that page what are worth a try for midterm practice.