Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
INTERPRETATION OF OBJECTIVE - S.CP.A.3
This objective introduces conditional probability and looks at how if two events are independent then P(A|B) = P(A). The previous objective connects directly to this one and helps to reinforce the concepts of independence.
(1) The student will be able to define independence using a conditional probability.
(2) The student will be able to determine if the probabilities probability is independent or not.
(3) The student will be able test if events are independent or not by checking if P(A|B) = P(A).
THE BIG IDEA
Once again independence is the big idea. A conditional probability means that an event has already taken place before the given event. In this type of environment it is of course essential to know if those two events were independent of each other because if they weren't the second probability will be altered in some way.
TRAPS & PITFALLS
The notation is new and bit of a bear...... Students who struggle with the concepts often got caught up on the new notation and never made it very far past that. Again I think again to do as much Venn diagramming will help out.
The student needs to come with the understanding of independence from the previous objective. We need to know that P(A) • P(B) = P(A and B) so that we can establish that P(A|B) = P(A and B)/P(B) = P(A).
In objective S.CP.B.8 we calculate conditional probabilities for both independent and dependent events. We will also use two way tables and from that data we will use these tests for independence.
MY REFLECTIONS (over line l)
Venn diagram... Venn diagram... I find that the more you have the student diagram these situations the more likely they are to be able to advance through the concepts. In this area I want them to understand that when we say GIVEN THAT event B has occurred means that we are only in event B and that the ONLY chances for event A to occur are found in the intersection of A and B, P(A and B).