Selecting an activity
- What is the probability that a guilty person is accused?
- What is the probability that an accused person is guilty?
This scenario has exactly the same mathematical structure as ‘The dog ate my homework’. Some key questions are:A particular medical condition is known to affect one in 1000 of the general population. A new test has been developed to screen for the condition.
- The test always gives a positive or negative result.
- The test will correctly give a positive result for 99% of people who have the condition
- The test will give an incorrect positive result for 2% of people who do not have the condition
- What is the probability that a person with the condition receives a positive test result?
- What is the probability that a person who receives a positive test result actually has the condition?
- What is the probability that a person who receives a negative test result actually has the condition?
- The probability that someone with a positive result actually has the condition is less than 5%
- The chances that someone who is given the all-clear turns out to actually have the condition, are about 1 in 100 000.
- Firstly, any medical scenario obviously needs to be handled with sensitivity – our ‘Dog ate my homework’ setting is deliberately light-hearted, and should not lead to any difficulties.
- In terms of practicalities, ‘The dog ate my homework’ has been carefully planned so that the data collection exercise will give usable results. Testing for rare medical conditions is difficult or impossible to model using the system of spinners and cubes that we have described!
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