Complex Probability

I love simple probability but complex is a bit harder to do because many students have difficulty with the idea of recalculating probability for each case.  I admit when I was in high school and had the topic, I wondered why if you had two bags and selected from one bag why you needed to worry about the one you weren't using.  It wasn't until college I realized one of the probabilities was choosing one of two bags.

My high school teacher didn't explain much in detail because he thought it should be obvious to us as we looked at the situation.  I always hated the "Its Obvious" train of thought.

One nice way to introduce the idea of complex probability is to use the video Menu Tossup which looks at calculating the total number of combinations on the menu.  Something students can easily relate to since they like eating at any of those fast food places.

Another way to show more about complex probability is to set up a probability bingo game.  The math equals love site has a great explanation of the game and where it originated. The idea is to fill out a bingo card covered with various combinations such as blue/green, green/red, red/blue, green/green, blue/blue, or red/red.  Students tend to prefer playing games to completing worksheets.

In addition, you could create or purchase compound probability task cards which can be placed around the room so students can get movement while working their way through the activity.  You could also create QR codes with compound probability questions or create or buy a compound probability scavenger hunt.

Scholastic has a nice little unit on compound probability with everything needed to teach the lesson including the 5 accompanying worksheets.  Its geared for 6th and 7th grades but it could easily be used in the high school, especially if working with ELL students.  It has students use a tree diagram to help derive the formula.

On the other hand, Better Lesson a nice lesson for 7th graders to learn more about complex probability and sample space.  In addition, it has students determine probability using an arithmetic strategy.

Unfortunately, many times including probability and statistics in the Algebra, Pre-Algebra, or Geometry classes is a bit hard because they do not fit nicely into the flow of the classes.  The topic is almost a disruption in the flow but I save it for short weeks like Thanksgiving, the end of the semester, spring break where a natural break falls in the class.

Let me know what you think, I'd love to hear.  Have a great day.