Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
INTERPRETATION OF OBJECTIVE - S.CP.A.2
This objective is all about independence and how if the two events are independent then P(A) • P(B) = P(A and B).
(1) The student will be able to explain what independence between two event means.
(2)The student will be able to determine if two events are independent of each other using P(A) • P(B) = P(A and B).
(3)The student will be able to define and distinguish between mutually exclusive and independent.
THE BIG IDEA
Independence is the BIG IDEA. Independence is a very important concept to understand in probability because once you begin doing more than one event in succession we need to know how the first event affected (if at all) the second event.
TRAPS & PITFALLS
Mutually exclusive and independence have ALWAYS been confused. Our English translation of independent is to be alone or separate which seems like the same thing as mutually exclusive BUT the English definition IS NOT the mathematical one. Independence is about affecting other events. Distinguish the early one or for sure you will have many confused later.
The student needs to have a good grounding in outcomes as subsets that can be described as intersections, unions and complements. We will connect P(A and B) be found in the intersection.
Independence continues for a few objectives. We look at in conditional statements next and then again in two way frequency tables. Independence is a major theme of this unit!
MY REFLECTIONS (over line l)
I moved quickly through this objective last time and it came back to bite me. When I got into the more difficult independence questions even my very best students were asking a lot of conceptual questions. I discovered it was because I hadn't connected the Venn diagram to P(A) • P(B) = P(A and B) very well. I have created a number of questions to build this understanding this time around.