Teacher Notes    

CONCEPT 1 – Compound Probabilities and Conditional Probability

As mentioned in an earlier objective when we do more than one event in succession (a compound probability) we have to concern ourselves with whether these events are independent or not.

We now have two multiplication rules for these two cases:


INDEPENDENT                         P(A and B) = P(A) • P(B)


NOT INDEPENDENT                P(A and B) = P(A) • P(B|A)

                                                       P(A and B) = P(B) • P(A|B)


When events are independent then P(A and B) = P(A) • P(B).


Let us look at some more examples of when the two events are dependent.



When events are not independent then P(A and B) = P(A) • P(B|A)


This is a nice way to relate the two formulas related to independence. We see that the one leads to the other. Students need to feel comfortable with both of these formulas to determine independence.


CONCEPT 2 – Formula connectivity


When we learned conditional probability we determined that: