MA/STAT416: Probability
Lecture Notes
Spring 2011
1
Chapter 3: Conditional Probability and Independence
February 9, 2011
3.4
More on Bayes’ Theorem
1.
Blood Tests.
A certain blood test for a disease gives a positive result 90% of the
times among patients having the disease. But it also gives a positive result 25% of
the times amon people who do not have the disease. It is believed that 30% of the
population has this disease. What is the probability that a person with a positive
test result indeed has the disease?
2.
Politics.
75% of Democrats and 25% of Republicans are prochoice.
In the
population, 48% are Democrats and 52% are Republicans.
If Cathy is prolife,
what is the probability that she is a Republican?
3.
Multiple Choice Tests.
Suppose that the questions in a multiple choice exam
have five alternatives each, of which a student picks one as the correct alternative.
A student either knows the truly correct alternative with probability 0.7, or she
randomly picks one of the five alternatives as her choice.
Suppose a particular
problem was answered correctly.
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 Spring '08
 Staff
 Conditional Probability, Probability, Cathy

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