Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in terms of the model.
INTERPRETATION OF OBJECTIVE - S.CP.B.7
This objective is quite direct. Apply the addition rule and understand it through Venn diagrams.
(1) The student will be able to calculate probabilities using the Addition Rule of probability.
(2) The student will be able to understand the Addition Rule of probability through Venn diagrams.
THE BIG IDEA
The addition rule is about understanding the union of two events. Venn diagramming greatly helps students visualize why the intersection needs to be subtracted out.
TRAPS & PITFALLS
As mentioned in the reflections the biggest issue is simply students moving too quickly and not thinking about 'overlap' or in other words the intersection. For example, what is the probability of getting a diamond or a face card in a standard deck? Students add 13/52 and 12/52 and don't think about that the Jack H, Jack D, Queen H, Queen D, King H and the king D all go double counted. Requiring Venn diagrams early on help to lessen this error.
The understanding of union and intersection are very important here. These concepts get build in objective S.CP.A.1 when we look at describing outcomes as subsets.
The Addition Rule for probability is used anytime more than one event can be a successful outcome.
MY REFLECTIONS (over line l)
This relationship is quite easy and students get it as long as it is presented with a Venn diagram. The sad thing is that when performing this calculation too many students don't think about the intersection - they simply add the two probabilities. For this purpose I have increased the number of Venn diagrams required with this type of problem.