Today we continued exploring conditional probability, independence, and the relationship between the two. We tackled another investigation from Navigating Through Probability. In this case the Independent or Not Independent task.
This task looks at identifying an association between students with asthma and students living within a smokers' household. Overall the class went well. Students were being thoughtful about what they were doing and were asking relevant questions that would push them toward a solution. Students definitely appear to becoming more comfortable with the notation, although several still struggled with how to describe the meaning of P(A | B).
The biggest hang-up can when explaining the meaning (the implication) of when P(A | B) and P(A) are not equal. Several latched onto the idea that the events are not independent but were hard pressed to explain why this result indicates independence.
With a little questioning and guidance, students started to see that the perception of likelihood of living in a smokers household changed when they knew a person had asthma versus not knowing anything about the individual. This influence of one event (having asthma) on the probability of a second event (living with smokers) is why the two events are not independent.
We'll continue to explore this through a couple of more examples before moving into probability models and expected values.
Visit the class summary for a student perspective of the class and to view the lesson slides.
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