IPS - Day 10

Today we looked at representing probability spaces using Venn diagrams. Most students have used Venn diagrams for classification purposes in science or social studies classes but very few have used them for probability. I spend a few minutes displaying a Venn diagram and discussing the components.

After this brief introduction, we started with a simple example for a deck of cards. I asked students to try and draw a Venn diagram that represented the two events of drawing a face card and drawing a heart. I allowed students to work on these and discuss in their groups. We presented some results on the board and discussed the representations.

Venn diagrams always pose a problem because sometimes information is presented where the values in the circles double count the overlap of the two events and sometimes the values do not include the overlap. I encourage students to write both values and distinguish the value that is not including the overlap as "Only."

I next provided a table of information for ear-piercing by gender. The table provided counts for those who did and did not have pierced ears. I asked students to represent this data in a Venn diagram. This problem always proves challenging because the inclination for students is to designate one circle for males and one for females. I then ask what the overlap of the two circles represent. They want it to represent either pierced ears or non-pierced ears.

It takes a few questions to get them to realize that their overlap represents individuals that are both male and female. It takes a little more time for them to realize (or from some coaching) that one circle needs to represent a gender and one piercing. At this point they can readily construct their Venn diagram and answer different probability questions using the diagram.

The class then worked on several practice problems. These problems allowed students to solidify the concepts for constructing and working with Venn diagrams.

I had students write in their notebooks things they wanted to remember when constructing and using Venn diagrams.

View the class summary for a student's take on the class and to see the lesson slides.