# Are My Rules Mutually Exclusive?

Awhile back, I read Sarah Carter’s post about the Guess My Rule activity she used at the start of the school year to build her group work norms for her classes. I really need to do a better job of building these in my own classes next year, but that’s another post. More recently, I saw her post about using these rule cards again with Venn Diagrams

My Algebra 2 students were right in the beginning of their last unit on counting principles and probability when I read this post, and I knew it would be perfect for us to practice the definitions of mutually exclusive / inclusive and the probability addition rules that go with each of those cases.

I really like doing activities that leave some parts of the problem up to chance, so that the answers don’t always come out “nice” or “normal” (I hate those terms, too. In this case I mean that some of the probabilities were often zero or 100%). I think that addressing these sorts of problems in their practice helps better prepare them for any sort of problem that may come at them, even when tests and other assessments normally have “nice” answers. It also forces them to really consider definitions as they work.

So, the first part of their task was to draw two of the rules cards and set up a Venn Diagram of the intersection. They had to decide if the rules were mutually exclusive or if they were inclusive, then use the proper probability rule to calculate the probability of rule 1 OR rule 2 being true out of the deck.

You can actually see the student worksheet that I made to go with this really well in this first picture, to see how they recorded their work.

Here’s one that was mutually exclusive:

We were also working on complements of events. For this one, they were asked to set up a Venn Diagram with THREE rules from the deck. Then, I asked them to describe the complement of one of the rules being true, and to find its probability. In retrospect, I should have changed a few things about this part of the activity. First, the labels for the rules need to go by the circles. My students really struggled with transferring their Venn Diagram numbers to their papers because they couldn’t keep track of which rule was which circle, especially if they had drawn their Venn Diagram in a different rotation than the one on their paper.

Second, I made the descriptions of the events too vague, so students really struggled with describing the complement.

I do think this activity was really helpful for my students to practice definitions of mutually exclusive, inclusive, and complement, and to practice using some probability rules!

I’ve uploaded the original file I used here, and a new version with the changes I made after doing the activity here. You can find the Guess My Rule cards in Sarah’s original post here.