Types of sample spaces

• A countable number of events (can be finite or infinite). For example, the sample space for flipping a coin twice is

  

• The sample space includes a range of values. For example, suppose a final exam is given from 2:00-4:00 p.m. The sample space for the time a student hands in the exam is

  

NOTE: By countable, we mean either a finite or infinite number of elements that can be counted. For example, is a finite countable set and is an infinite countable set. Any infinite sequence that we can associate with the numbers is also (infinitely) countable, e.g., or . Note that the sample space in the second example is uncountable.