TB
No TB
ID used
11
96
ID not used
35
1850

14
EXTRA PROBLEMS
85
Estimate the relative risk of developing TB in relation to the use of intravenous drug use from
this study and interpret the result.
4. Suppose in a group of recent graduates, it was found that 28% had a law degree and 17% had
a MBA. Five percent had both of these degrees.
What is the probability that a randomly
selected graduate has a MBA if they do not have a law degree?
5. A study was conducted to investigate a new procedure for detecting renal disease in patients
with hypertension.
Using the new procedure, experimenters screened a random sample of
200 hypertensive patients. Then the presence or absence of renal disease was determined by
another method. The data obtained are shown in the following table:
Disease Absent
Disease Present
Disease Detected by the New Procedure
16
21
Disease Not Detected by the New Procedure
157
6
What are the false-positive rate and false-negative rates for the new procedure?
6. We are interested in studying the survival rate of the marmot population on Mt. Washington.
A marmot must survive last year to be encountered this year.
Assume that survival and
encounter probabilities are constant, the probability of surviving and being encountered is
0.40, and we encounter a marmot with probability 0.58.
What is the probability that a
marmot survives the year?
14.5
Set 6 Mutually exclusive and independence
1. Each member of a certain population of unhealthy patients has a risk of heart attack at levels
low, medium, or high; and a risk of stroke at levels low, medium or high. The proportions of
patients within each of the 9 categories are given in the following table.
Risk of
Risk of stroke
heart attack
Low
Medium
High
Low
0.13
0.15
0.12
Medium
0.02
0.30
0.08
High
0.05
0.05
0.10
(a) Suppose that one patient is randomly chosen from this population. If the chosen patient
has a medium or high risk of heart attack, what is the probability that the patient has
only a low risk of a stroke?
(b) Suppose that one patient is randomly chosen from this population. Which of the following
statements are true?
i. The events chosen patient has a low risk of heart attack and chosen patient has a
high risk of stroke are independent.
ii. The events chosen patient has a medium risk of heart attack and chosen patient has
a medium risk of a stroke are mutually exclusive.