Intent

In this activity, students make a list of all possible cases, giving them a clear picture for finding probabilities.

Mathematics

Using systematic lists, students can find probabilities by counting possible outcomes and applying the basic definition of probability:

Progression

Students are introduced to another tool for finding probabilities.

Approximate Time

Brief introduction

20 minutes for activity (at home or in class)

15 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Doing the Activity

As a class, read the introduction to Paula’s Pizza aloud. Clarify that all pizzas must have two different toppings; no pizza can be “double” pepperoni or “double” anything.

Students will probably want to make a list of all possible two-topping combinations. Encourage them to be systematic, perhaps listing all the combinations with sausage, then those with onions (and not sausage), and so on. There are several ways to organize this list to ensure that no two-topping pizza is overlooked and that there are no duplicates.

Discussing and Debriefing the Activity

Encourage students to compare their results. Did everyone find all the possible combinations, without duplication? With the list of 15 possibilities, students should realize that Paula’s probability of getting the pizza she ordered (Question 2) is 115115 size 12{ { {"1"} over {"15"} } } {} and that her probability of getting something different is 14151415 size 12{ { {"14"} over {"15"} } } {}. If students do not notice that these two probabilities add to 1, ask questions to help lead them to this observation.

In Question 3, students just need to count that there are six combinations that include neither sausage nor pepperoni. They can then conclude that the probability of Paula getting a pizza she likes is 615615 size 12{ { {6} over {"15"} } } {} and the probability of her getting a pizza she doesn’t like is 915915 size 12{ { {9} over {"15"} } } {}.