7D In-Class Activity

Medical tests designed to detect diseases are not always perfect.

Sometimes, people who get tested may be told they have a disease when they do not actually have the disease.

Other times, people who get tested may be told they are free of a disease when in fact they have the disease.

Credit: iStock/wildpixel

The goal is for medical tests to be correct as often as possible so that these types of errors are rare.

Question 1

In your opinion, what is worse—telling someone they have a disease when in fact they do not OR telling someone they do not have a disease when they actually do?

COVID-19 Test Reliability

Question 2

A testing facility reports the following testing reliability results for their COVID-19 test:

80% of the people tested in the facility do not have COVID-19.
2.25% of people who do not have COVID-19 test positive for it.
80% of people who have COVID-19 test positive for it.

We want to answer the following questions:

If someone tests positive for COVID-19, what is the probability they truly have it?
If someone tests negative for COVID-19, what is the probability they truly do not have it?

Begin by labeling the highlighted rows and columns in the following table.

Positive test Total

Does not have COVID-19
Complete the table (including row and column totals) based on the previous information and a hypothetical 1,000 people.

Question 3

Question 2, Parts a and b will help you answer the following question: “If someone tests positive for COVID-19, what is the probability they truly have it?”

Write the desired probability in words by filling in the blanks: [latex]P(___________ GIVEN ___________)[/latex]
Find the probability to the nearest ten-thousandth.

Question 4

Question 2, Parts a and b will help you answer the following question: “If someone tests negative for COVID-19, what is the probability they truly do not have it?”

Write the desired probability in words by filling in the blanks: [latex]P(___________ GIVEN ___________)[/latex]
Find the probability to the nearest ten-thousandth.

A certain pregnancy test detects 90% of pregnancies. It gives a negative test result to 99% of people who are not pregnant. A scientist decides to study pregnancy probabilities from this test. In her study, 30% of the study participants are truly pregnant.

Question 5

Construct and complete a table using a hypothetical 1,000 people.

Question 6

If a randomly selected study participant receives a positive test, what is the probability they are truly pregnant?

Question 7

If a randomly selected study participant receives a negative test, what is the probability they are truly not pregnant?

Question 8

Construct and complete a table using a hypothetical 1,000 people.

Question 9