Milo Schield ([EMAIL PROTECTED]) wrote:
: What kinds of questions or exercises (either abstract or particular) would
: be good ways of measuring a student's understanding of conditional
: probability?
"Court records indicate that 66% of persons convicted of crimes in
Hoogledash Country are black. Therefore, if a Hoogledash County police
officer encounters a black person, there's a 66% chance that he's dealing
with a criminal. True or False?"
"The population of Puppernack county is entirely black. Court records
show that all persons convicted of crimes in Puppernack County are
residents of the county. Therefore, if a Puppernack County police
officer encounters a black person, he's certain to be dealing with a
criminal. True or False?"
Students who answer false to both have a basic understanding of
conditional probability. Students who answer true to both are probably
unable to distinguish between P(A|B) and P(B|A). Students who answer
true to the first question and false to the second question may have some
understanding of the difference but lack certain critical thinking
skills. Students who answer false to the first question and true to the
second probably have problems with reading comprehension.
Discussion item, after students are convinced that both questions should
be answered false: What further information would they need in order to
determine the probability that the officer was encountering a criminal?
After discussion, introduce simplified form of Bayes' Theorem:
P(A|B)=P(B|A)*P(A)/P(B). Have students work examples where P(A|B) close
to P(B|A) and where the two probabilities are far apart.
Then ask the classic question about mass HIV screening and introduce the
concepts of sensitivity and specificity (concrete concepts that students
can relate to the abstract concepts of conditional probability).
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
