Discrete Math - Day 20

Today we practiced working with Bayes theorem. The first task was helping students to decode text to understand what events to use and what probabilities to determine.

I presented a structure for students to consider and asked them to work through identifying the components they would need to use to answer the question. As anticipated, there was a lot of confusion and misunderstanding they arose when attempting this. This led to a good class discussion about how to identify components.

The next task was actually calculating the necessary probabilities. This involved taking weighted averages, which again caused problems with students. There were good questions about why you simply couldn't add two values together and divide by two, whether the probability was for an overall rate or just for a specific event, etc.

Students then tackled another problem. Although there continued to be confusion on identifying events of interest and how to calculate an accumulated probability, more students were feeling comfortable with how to proceed and how to resolve these issues. By the end of this problem, the majority of students were feeling more confident about working through a Bayesian probability problem. They admitted they didn't like doing it but they felt they could do it.

I briefly touched upon what they just worked on and how this relates to spam filters, explicitly connecting events and probabilities in the Bayes formula to the scenario.

Working through and discussing these two problems took over 60 minutes. Since there was only about 20 minutes left, I decided to pass out the take home quiz and give them time to work on it in class. The quiz covered counting concepts such as combinations, permutations, and pigeonhole problems.

View the class summary for a student's perspective of the class and to see the lesson slides.