Homework 3
Due Friday, April 19
Chapter 3: 25, 26, 30, 31,42
Chapter 4: 3, (note, probabilities derived this way are usually called "empirical
probabilities"),5,6,7,8,10
A. If two events are mutually exclusive, might they be independent?
(If yes, under what conditions? If no, explain) If two events
are independent, might they be mutually exclusive? (If yes, under what
conditions? If no, explain.)
B.
|
Disease
|
No Disease
|
Total
|
Disease Detected
|
90
|
5
|
95
|
Disease Not Detected
|
15
|
100
|
115
|
Total
|
105
|
105
|
210
|
A diagnostic test was developed to detect a rare and expensive disease. 105
healthy people and 105 people infected with this affliction were tested on
the procedure. The results are shown in the table above. Based on these
data, calculate the following probabilities. (Imagine selecting one
of the 210 people at random.)
a) P(Disease detected | have disease)
b) Suppose the doctor says you have the disease. What's the probability
you really do?
c) Are the evnets "have the disease" and "disease detected" independent?
Mutually exclusive?
Show work.
d) If we select one of these people at random, what's the probability
they have the disease and it was not detected?