A lot of people in my classes struggle with conditional probability. Don’t feel alone, though. A lot of people get this (and simple probability, for that matter) wrong. If you read Innumeracy by John Allen Paulos (Hill and Wang, 1989), or The Power of Logical Thinking by Marilyn vos Savant (St. Martin’s Griffin, 1997), you’ll see examples of how a misunderstanding or misuse of this has put innocent people in prison and ruined many careers. It’s one of the reasons I’m passionate about statistics, but it’s hard for me, too, because it’s not easy to work out in your head. I always have to build a table.

The best thing to do is to be completely process-driven; identify what’s given, then follow the process and the formulas religiously. After a while, you can start to see it intuitively, but it does take a while.

In my MBA stats class, one of the ones that always stumped the students was a conditional problem:

 …