12.3.2

Section 12.3.2 Blog Entry

Having read section 12.3.2 in the text:

Difficult:
In the very beginning of section 12.3.2 The Law of Total Probability, I was a bit confused on what the notation sample space omega = U from i=1 to n of Bi meant. It was labeled as (ii) on page 808. Do this just mean that each value of Bi from i=1 to i=n is the partition and you would add all of these up to form the sample space?

Reflective:
Once again, I think the use of multiple variables and notations made the material a bit confusing to understand and figure out in the beginning. When I first read the bottom of page 808 about letting A be an event and writing A as a union of disjoint sets using the partition of the sample space, I did not really understand how (A intersection B1) U (A intersection B2) U....U (A intersection Bn) could equal the same A, but when I looked at Figure 12.15, I think I was able to visualize the equation/problem better and understand what it meant. I think it was helpful for me to observe and think about the diagrams and figures that accompanied each example in this section. Also, in example 3, at first I was really confused at what the text was trying to determine because I don' t think I understood that it was making a distinction between testing positive for a disease because you actually have the HIV virus or because your test was misread also taking into account the actual prevalence of the disease in a population.