MAT 144 ADDITIONAL CLASS
PROBLEMS - BAYES THEOREM
AND DESCRIPTIVE STATISTICS
(SPRING 2025) LATEST UPDATE
WITH SOLUTIONS
Study Ace Smart
, Mat 144 Additional Practice Problems – Bayes’ Theorem; Introduction to Statistics
Feburary 2025
Prof. Baruch
Section One: Bayes’ Theorem
Example 1:
A leading medical journal at the University of X Medical School has published a
report that the percentage of the global population infected with a viral disease is
27.5%. A medical testing company, XYZ, has produced a test kit designed to detect
if the patient is infected with the disease. The company was able to have
volunteers getting tested (both who are infected and those who are not infected).
After testing their product, the company states that 98.5% of the patients who are
infected, were correctly tested positive. Furthermore, the company also states
that 97.8% of the patients who are not infected, were correctly tested negative.
Question (1):
A patient wants to get tested to find if he/she is infected. The patient went to a
clinic and took the test. The doctor informed the patient that he/she is not
infected with the disease. What is the probability that the patient is infected?
Question (2):
Another patient went to the clinic to get tested. The doctor informed that patient
that he/she is infected. What is the probability that this patient is not infected?
Question (3)
A third patient went to visit the doctor to determine if he/she is infected. The
result of the test indicates that the patient is negative. What is the probability
that the patient is not infected?
Example 2:
An auto manufacturer has five plants in production. The percentage of the total
output each plant contributes is 20%. Once the cars are built, the quality engineer
will inspect each of the cars to determine what is the defective rate in each of the
plants. At plant I, 2.5% of the output are defective. At plant II, 2% of the total
PROBLEMS - BAYES THEOREM
AND DESCRIPTIVE STATISTICS
(SPRING 2025) LATEST UPDATE
WITH SOLUTIONS
Study Ace Smart
, Mat 144 Additional Practice Problems – Bayes’ Theorem; Introduction to Statistics
Feburary 2025
Prof. Baruch
Section One: Bayes’ Theorem
Example 1:
A leading medical journal at the University of X Medical School has published a
report that the percentage of the global population infected with a viral disease is
27.5%. A medical testing company, XYZ, has produced a test kit designed to detect
if the patient is infected with the disease. The company was able to have
volunteers getting tested (both who are infected and those who are not infected).
After testing their product, the company states that 98.5% of the patients who are
infected, were correctly tested positive. Furthermore, the company also states
that 97.8% of the patients who are not infected, were correctly tested negative.
Question (1):
A patient wants to get tested to find if he/she is infected. The patient went to a
clinic and took the test. The doctor informed the patient that he/she is not
infected with the disease. What is the probability that the patient is infected?
Question (2):
Another patient went to the clinic to get tested. The doctor informed that patient
that he/she is infected. What is the probability that this patient is not infected?
Question (3)
A third patient went to visit the doctor to determine if he/she is infected. The
result of the test indicates that the patient is negative. What is the probability
that the patient is not infected?
Example 2:
An auto manufacturer has five plants in production. The percentage of the total
output each plant contributes is 20%. Once the cars are built, the quality engineer
will inspect each of the cars to determine what is the defective rate in each of the
plants. At plant I, 2.5% of the output are defective. At plant II, 2% of the total
