What Is the Probability That a Positive Test Indicates Actual Disease?

In summary, according to Baye's theorem, the probability of a random person testing positive and actually having the disease is 1/21, or approximately 0.048. This takes into account the low prevalence of the disease (0.1%), the false positive rate of the testing method (5%), and the fact that there are 50 false positives for every 1 real positive in a sample of 1,000 people.
  • #1
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Homework Statement



Approx. 1/1000 has a disease, and the method of testing has a 5 % false positive rate. If a random person tests positive, what is the probability that he has the disease?

Homework Equations



I'm pretty sure Baye's theorem is the thing to use.

The Attempt at a Solution



I'm having trouble defining my probabilities. I've defined that P(sick) = 0,001 and P(not sick|+) = 0,05. But then I'm stuck...
 
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  • #2
You could try the problem this way:

Let's say we test 1,000 people:
How many false positives do we expect to get?
How many real positives do we expect to get?
 
  • #3
Well, wouldn't that be 50 and 1?
 
  • #4
So, how likely is a positive test to indicate disease?
 

1. What is the probability of getting a disease?

The probability of getting a disease depends on various factors such as genetics, lifestyle choices, and environmental factors. It is not possible to give a specific number as the probability varies for each individual.

2. How is the probability of disease calculated?

The probability of disease is calculated using statistical methods and data analysis. This involves looking at the prevalence of the disease in a population, risk factors, and other relevant factors to determine the likelihood of an individual developing the disease.

3. Can the probability of disease change over time?

Yes, the probability of disease can change over time. Factors such as aging, changes in lifestyle, and new medical treatments can all affect the likelihood of developing a disease.

4. How can I reduce my risk of developing a disease?

There are several ways to reduce your risk of developing a disease. These include maintaining a healthy diet and exercise routine, avoiding harmful substances such as tobacco and excessive alcohol consumption, and getting regular check-ups and screenings.

5. Is there a way to accurately predict the probability of disease?

Predicting the probability of disease is not an exact science. While statistical methods and risk factors can give us an idea of the likelihood, there is no way to accurately predict whether or not an individual will develop a disease.

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