Lesson 4.2 – Basic Probability Rules
- Give a probability model for a chance process and use it to find the probability of an event.
- Use the complement rule to find probabilities.
- Use the addition rule for mutually exclusive events to find probabilities.
“Applebee’s OR” versus “Starbuck’s OR”
We started the lesson today with a short discussion about the word “OR”, which can have a different meaning in the English language than its mathematical meaning. At Applebee’s, when ordering the Triple Bacon Burger, the server will ask if you would like “french fries OR onion rings”. So you have the choice of getting french fries or onion rings (but not both). At Starbuck’s, when ordering your (bitter) coffee, the barista will ask if you would like “cream OR sugar”. This time you have the choice of cream only, sugar only, or both. So which one is correct? For probability calculations, we will be using the Starbuck’s OR.
We did question #1 as a whole group. Define this list of possible outcomes as the sample space. Also recognize that each of the outcomes is not going to be equally likely (once we have chosen our 10 students).
For question #2, we chose 10 students to come to the front of the room. Make sure that you choose at least one blue-eyed male and at least one brown-eyed female. Find totals for each possible outcome and turn counts into probabilities and then send students back to their desks.
For questions #3-5 students work in pairs. Question #4 should warrant the most discussion in the pairs. After students are given time to discuss and make predictions, we bring the 10 students back up to the front of the room so that we can check our answers.
For P(male OR female), we have all the males raise their hand and count them. Then have all the females raise their hand and count them. Then have any students that is “male OR female” raise their hand and count them. Students realize that P(male OR female) = P(male) + P(female). This is the addition rule for mutually exclusive events.
For P(male OR blue eyes), we have all the males raise their hand and count them. Then have all the blue eyes raise their hand and count them. Then have any students that is “male OR blue eyes” raise their hand and count them. Students realize that adding the number of males to the number of blue eyes does not work here because some students have been double counted (all the blue eyed males). So we need to subtract out the people who were double counted, or P(male or blue eyes) = P(male) + P(blue eyes) – P(male and blue eyes). This is a great context to introduce the idea of mutually exclusive and the general addition rule, which will be a learning target in Lesson 4.3.
It is important for students to get the visual of “double counting” when we have events that are not mutually exclusive. By having students physically raise their hands for each event, it is easy to see when a student is “double counted”. Remember who was double counted so that later in the chapter when students make a double counting mistake, you can remind them about the time when “Adam got double counted”.