Probability Rules (even if students don't think so)
Day 45 - Lesson 5.2
Give a probability model for a chance process with equally likely outcomes and use it to find the probability of an event.
Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.
Activity: Odds or evens, who will win?
When playing Odds or Evens be sure that students are finding the product of the two dice and not the sum. Most students will claim that Odds has a 50% chance of winning and Evens has a 50% chance of winning. As they are playing, ask them the point at which they started to be suspicious of their original claim. For the whole class results, we had students record the number of odds wins out of 20 on the board and we totaled them up (or they could input their values into an Excel document).
For groups that finish quickly, ask them how they might design a game that would be more fair.
This lesson introduces a second strategy for solving probability questions: sample space (remember simulation was the first). This strategy works well for situations where it is reasonable to list out the whole sample space (or even just think about all of the possible outcomes) and all of the outcomes are equally likely. Finding probability using the sample space becomes a simple counting exercise (NO FORMULAS!).
Experience First, Formalize Later
This lesson is a great example of students doing the thinking and reasoning before the teacher formalizes the learning. Students get a chance to use and think about sample space, the general addition rule, complement rule before we even use this vocabulary. The experience will allow students to internalize the learning and hold on to it long-term.