Segment

Time

 Collect Journals. Collect homework


Discuss Rodney King questions:
 Investigate whether "chance" is a reasonable
explanation for all pursuing officers being white?
 Suppose you are a member of the California Supreme
Court and that before you is the matter of what level of likelihood
may be taken as "evidence of racial bias in police dispatching
procedures." What level would you set for that and future cases?
 What does the idea of probability, or "behavior
in the long run," have to do with these questions?


Review:
 Process (experiment)
 Outcome
 Sample space
Exercise 2.10 (p. 16). What is the process? What
is an outcome? What is the sample space?


Discuss homework (HIV):





 Translate HW question: What fraction of the those
people who test positive actually have HIV?


TEST YES

TEST NO


HIV

HIV YES

98% of 0.5%

2% of 0.5%

HIV NO

2% of 99.5%

98% of 99.5%




Take a visual approach:


US Census Bureau table. Ask, for example, these questions:
 What fraction of the US population is White? Black?
Native?
 What fraction of the US population is Hispanic?
Black Hispanic? Native Hispanic?
 What fraction of Native Americans are Hispanic?
What fraction of all Hispanics are white?
 I say, "Pick a US citizen at random. What is the
probability this person is Native American?"
 What does this mean? (When you pick a person
at random many times, what fraction of those times …)
 Why can we say this? (We expect the composition
of large simple random samples to reflect the population's composition.)
KEY!!!! (Large samples are made by picking individuals one at a time!)
 I say, "Pick a Hispanic person at random. What
is the probability this person is Asian?
 What does this mean? What is your answer?


Homework (Tomorrow, Friday, show the table also and
then the tree diagram as a shortcut to the table and diagram. But STRESS
that the tree diagram is not a SUBSTITUTE for the others. Rather, it is
a way to reason the same way without having to write so much down.


My intention for these questions is to have students
start thinking in this way:
That is, students now tend to think of probability
of events over the long run, but each event has its own "long run." When
they think that way, then they cannot see a link between longterm behavior
and sample space. Rather, they understand the link between longterm behavior
and sample space when they understand that the longterm behavior of a
process in relation to one outcome entails relationships to the other
possible outcomes, too. So, we need to emphasize that we need only
think of one longrun sequence of trials in order to imagine the probability
of any of the processes possible outcomes. When every outcome has
its on longterm repetition of the process, then there is no way to imagine
each in relation to the other. The longruns are, in a sense, independent
of each other. They need to be imagined in relation to each other, and
imagining them all being contained within a single long run of the process
does that.

