Contents

Quiz 6: Probability theorems

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Quiz

This quiz tests materials in the section called “Probability theorems”. If you are struggling with the questions go back and re-read 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 0-12, 10-19 years

  • Age groups 0-5, 6-9, 10-19, 20-25 years

  • Age groups 0-3, 4-13, 14-19 years

  • Age groups 0-5, 6-9, 11-14, 15-19 years

Choose the correct answer:

  1. All four are partitions

  2. Only the third option is a partition

  3. The third and fourth are partitions

  4. None of them are partitions

The following table shows results from a population-based 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:

  1. \(0.15\)

  2. \(1\)

  3. \(0.4\)

  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 face-to-face 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 (face-to-face 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:

Face-to-face

Telephone

Video consultation

Face-to-face

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 face-to-face appointments as their main contact in 2010?

Choose the correct answer:

  1. \(0.4\)

  2. \(0.3\)

  3. \(0.2\)

  4. \(0.1\)

Quiz 5: Probability Quiz 7: Discrete Random Variables