Lesson 4.3 – Two-Way Tables and Venn Diagrams
- Use a two-way table to find probabilities.
- Calculate probabilities with the general addition rule.
- Use a Venn Diagram to find probabilities.
What does the word “AND” mean?
We started with a short discussion about the mathematical meaning of the word “AND”. We used the context of “Senior AND going to college”. We decided that the event “A AND B” means that event A is true and event B is true. We also reminded students that in mathematics, we use the Starbuck’s OR.
Activity: Facebook or Twitter?
We started by having all the students come to the front white board to put a tally mark in the appropriate location. Then we counted up the tally marks. From there, students worked in pairs on the rest of the Activity. We made the suggestion to students to write all probabilities as fractions.
Question #5 will give students the most trouble. We always suggest that the first number that should go into a Venn Diagram is the overlap (Facebook and Twitter). It is also important that students recognize that the total sum of all the numbers in the Venn Diagram should be the total number of students in class.
The most common student mistake with Venn Diagrams is the number they record for “Facebook and not Twitter”. Students will very often mistakenly record the total count for “Facebook” here (17) instead of “Facebook and not Twitter” (7). Remind students that the total within the left circle must be 17.
It is very important that students see where each number from the two-way table can be seen in the Venn Diagram (yes, even totals). We use different color whiteboard markers to represent each section in the Venn Diagram. The event “Facebook and not Twitter” is the left Pacman (black). The event “Facebook and Twitter” is the overlap in the center. The event “Twitter and not Facebook” is the right Pacman (red). The event “Facebook or Twitter” is shown in green (remember the Starbuck’s OR says it could be Facebook only OR Twitter only OR both).