Reading this piece general public piece on conditional probabilities brought me back more than 17 years ago back when in my senior year in college I was being introduced to conditional probabilities. Indeed in the manner it was taught it was seen as impenetrably daunting and really hard to relate to anything practical. But overtime as I have assimilated the theoretical and practical use of conditional probabilities, I must say the formal approach, once assimilated is very mechanical in helping produce accurate estimations. What is often confounding in making estimates based on conditional probabilities, is that the language used corrupts thoughts. That is why examples such as the Monty Python one and the Mammogram results interpretation are so confounding to educated and otherwise intelligent people.
It seems to me educational curriculums should focus on teaching the intuitive and formal approaches simultaneously and move towards pointing out when the intuitive approach finds its limitations and must be overtaken by the more formal one.
I also realize how BICs as extensions and generalizations of the concept of conditional probabilities must be patiently taught to be better understood over time
References:
Chances Are, By Steven Strogatz. Opiniator piece in the NY Times 04/25/2010
BICs
The Wider Scope of BICs
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