101-102 Cross Sectional Volumes and A Very Important Statistics Lesson Split

Tis the time of year when the IB students learn some different stuff than the AP BC kids.

AP Calc BC

Cross-sectional volumes. This quick demo worked just fine. Also had a bunch of 3D printed models to show, but the paper on board technique worked nicely.


IB Math HL

We also did this exact same example in PreCalc H that day (who is also doing prob/stats). A great motivator for why just about everyone in the room should know how this stuff works. I’d bet everyone in the room has a family member who has already been, or will be affected by cancer.

Here’s the setup:

A blood test has been developed to detect cancer. The probability that the test correctly detects someone with cancer is 0.97. The probability that the test correctly identifies someone without cancer is 0.93. Approximately 0.1% of the population has this cancer.
Question: You walk in to the doctors and take this test. It comes up positive. What is the probability that you have cancer?

What a great lead-in to Bayes Theorem. Give it a second, what would you guess the answer is?

Here’s the Bayes method of solving the problem. A bit strange and abstract. Hard to handle.

Still, an amazing result. Only 1.4% of the people who test positive actually cancer???????

Lets make this more concrete: Take a population of 1,000,000 and walk through the actual amount of people who have cancer etc…

I like that so much better. Same math, but so much easier (for at least me) to understand.





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