Quiz 6: Probability theorems¶
If you wish, you can do a self grading version of the quiz below. In order to open the interactive version of the notebook, you need to open it in Binder. To do this, hover your mouse over the rocket symbol (near the top right of the page) and click on the word “Binder” which should appear. This will load an interactive quiz. The first time you load this it may take a few minutes.
Quiz¶
This quiz tests materials in the section called “Probability theorems”. If you are struggling with the questions go back and reread the relevant material.
Question 1: If the sample space is ages (to nearest year) of people under 20 years old, which of these groupings form partitions of the sample space?
Age groups 012, 1019 years
Age groups 05, 69, 1019, 2025 years
Age groups 03, 413, 1419 years
Age groups 05, 69, 1114, 1519 years
Choose the correct answer:
All four are partitions
Only the third option is a partition
The third and fourth are partitions
None of them are partitions
The following table shows results from a populationbased survey about respiratory health.
Smoking status 
Relative frequency 
Proportion with asthma 

Former 
0.35 
0.20 
Current 
0.20 
0.15 
Never 
0.45 
0.05 
Question 2: What is the probability that a randomly selected individual from this population has asthma?
Choose the correct answer:
\(0.15\)
\(1\)
\(0.4\)
\(0.1225\)
Electronic health records were used to establish the main medium of contact for each patient with their GP during the year 2020 and the year 2010, in order to explore changes in health service use.
In 2010, 80% of patients used facetoface appointments as their main contact with their GP. Results for 2020 are displayed in the table below. Patients are grouped by their main GP contact method in 2010 (facetoface or telephone). The numbers shown are conditional probabilities of using each method of contact in 2020, given their method of contact in 2010.
In 2010 
In 2020: 
Facetoface 
Telephone 
Video consultation 

Facetoface 
0.9 
0.05 
0.05 

Telephone 
0.1 
0.6 
0.3 
Question 3: A patient from this population attends a video consultation in 2020. What is the probability that that same patient used to have facetoface appointments as their main contact in 2010?
Choose the correct answer:
\(0.4\)
\(0.3\)
\(0.2\)
\(0.1\)