CONCEPT 1 – Probability in Everyday Life

Do you like basketball because you are from New York or are you from New York because you like basketball?  Are you hungry because you thought of Panda Express or did you think about Panda Express because you are hungry?  Do you like playing video games because you are a teenager or because you like video games you are a teenager?  Do boys listen to different music than girls?  Is music listening independent of gender?  Is favorite color independent of gender?  Is there a connection between type of phone and hair color?

In this objective we want students to gather data to make some conclusions about independence or dependence of events.  The question is:  Does one event influence the other?

There are many things that we could compare and ask about their relationship.  The goal of this objective becomes two-fold.  One, we want student to be able to recognize the concepts in terms of everyday language.  We want students to think critically about the relationships.  Just because dependence might be found, we need them to understand that other variables and events could also be in play creating this result.  This is a common problem with analysis; sometimes there are lurking variables that are hidden to the individual.  For instance, after using a drug many of the individuals may claim to feel better.  The observers sees a direct correlation… use of drug, feeling better… but maybe during the study the weather swung from cool and cloudy to warm and sunny and that many of the peoples answers stemmed from the weather change and not the drug. Just because a cause-and-effect relationship appears to exist doesn't mean there is one necessarily.

In our example earlier, were we hungry because of our thought of Panda Express or did we think of Panda Express because we were hungry?

Second, we want students to be able to explain their findings.  To be able to take the data and represent it into a Venn diagram or two-way frequency table so that they can easily determine the relationships.  In this form students will be able to determine specific probabilities and independence.
Students can put to together an action plan to gather the data – a survey or questionnaire to a group of people and then draw analysis concerning independence and relationships.

From your results, you could create a two-way table. You could ask the same questions in the opposite order, as well, and create a similar two-way table.

Once you have your two-way table, you can calculate individual probabilities. From those, you can get conditional probabilities, and from those, you can estimate if two events are independent or dependent.
The most important key in this lesson is to teach students to think critically about the questions they want answers to. From this, students should be able to link their questions to the types of data they will gather. Finally, they should be able to assemble the data and infer relationships from the data using their knowledge about probabilities.