Introduction to bayes theorem and medical testing.

1. Suppose a test for cancer is known to be 98% accurate. This means that the
outcome of the test is correct 98% of the time. Suppose that 0.5% of the
population have cancer. What is the probability that a person who tests
positive for cancer has cancer?
Suppose 1 000 000 randomly selected people are tested. There are four
possibilities:
• A person with cancer tests positive • A person with cancer tests negative
• A person without cancer tests positive • A person without cancer tests negative

2. Suppose a test for cancer is known to be 98% accurate. This means that the
outcome of the test is correct 98% of the time. Suppose that 0.5% of the
population have cancer. What is the probability that a person who tests
positive for cancer has cancer?
(1) (a)How many of the people tested have cancer?
(b) How many do not have cancer?
(2) Assume the test is 98% accurate when the result is positive.
(a) How many people with cancer will test positive?
(b) How many people with cancer will test negative?
(3) Assume the test is 98% accurate when the result is negative.
(a) How many people without cancer will test positive?
(b) How many people without cancer will test negative?
(4) (a) How many people tested positive for cancer?
(b) How many of these people have cancer?
(c) What is the probability that a person who tests positive for cancer has
cancer?

3. Suppose a test for cancer is known to be 98% accurate. This means that the
outcome of the test is correct 98% of the time. Suppose that 0.5% of the
population have cancer. What is the probability that a person who tests
positive for cancer has cancer?
(4) (a) How many people tested positive for cancer?
(b) How many of these people have cancer?
(c) What is the probability that a person who tests positive for cancer has
cancer?

4. Suppose a test for cancer is known to be 98% accurate. This means that the
outcome of the test is correct 98% of the time. Suppose that 0.5% of the
population have cancer. What is the probability that a person who tests
positive for cancer has cancer?

5. Suppose a test for cancer is known to be 98% accurate. This means that the
outcome of the test is correct 98% of the time. Suppose that 0.5% of the
population have cancer. What is the probability that a person who tests
positive for cancer has cancer?

6. Suppose a test for industrial disease is known to be 99% accurate. This means
that the outcome of the test is correct 99% of the time. Suppose that 1% of the
population has industrial disease. What is the probability that a person who
tests positive has industrial disease?