3/7/00 lesson plan

Intent of lesson: to practice different ways of thinking about conditional probability statements.

Relate discussion to previous assignments: US demographics, Vandy student population, HIV drug test situations.

Be able to do 2 things:

  1. formalize conditional probability statements/situations
  2. interpret "P[A|B]" in probabilistic terms


Notation P[A|B] denotes a conditional probability statement:

"Given condition B, what is probability of A?" or "What is probability of A given condition B?" (explain convention of this notation).

Ways to think about what this means:

If you’re thinking of a population and of how it is composed, then think of P[A|B] as "if you restrict your attention to sub-population B, then P[A|B] is the fraction of the Bs that are As"

If you’re thinking of collecting a sample by drawing elements at random one at a time from population, think either of

  1. restricting your selection from sub-population B and ask "what fraction of the time that you select at random from B do you get A?"
  2. once sample has been collected, look only at those elements in it that are Bs. Then ask "what fraction of those Bs are As?"