Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
INTERPRETATION OF OBJECTIVE - S.CP.B.6
This objective builds from the earlier objective S.CP.A.3 that established the basic conditional relationship of P(A|B) = P(A and B)/P(B). In this objective we begin to calculate values and also work with both dependent and independent events.
(1) The student will be able to calculate conditional probabilities for both independent and dependent events.
(2) The student will be able to understand conditional probability through Venn diagrams.
THE BIG IDEA
To work with a sequence of events you must determine whether the events are independent or not. This objective builds on the earlier one by adding calculation of both independent and dependent events.
TRAPS & PITFALLS
Poor understanding of Venn diagrams and the intersection make visualizing and understanding conditional probabilities more difficult. As you teach this area use Venn diagrams regularly.
This objective relies on S.CP.A.3 where conditional probability was first introduced. The concepts there and the focus on independence allow students to deal with the more complex situation when events are dependent.
Compound probabilities rely heavily on determining independence or not and the use of conditional probability calculations.
MY REFLECTIONS (over line l)
I assumed that my students had seen some of this and that it wouldn't be too difficult. I found that very few had much probability experience and conditional probabilities and their calculations came to be difficult. I found myself reteaching and when I would I used Venn diagrams more often and that seemed to really help.