## A Diagnostic test has a 98% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probabili

A Diagnostic test has a 98% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probability of giving a (false) positive result when given to a person who does not have the disease. It is estimated that 15% of the population suffers from this disease. (a) What is the probability that a test result is positive? (b) A person receives a positive test result. What is the probability that this person actually has the discase? (c) A person receives a positive test result. What is the probability that this person does not actually have the disease?

## Answers ( )

Answer:a)

b)

c)

Step-by-step explanation:For this case we define the following notation:

+ represent the event of getting a positive result

D = represent the event of having the disease

ND = represent the event of NO having the disease

From the info given we know that:

And by the complement rule we can find:

Part aFor this case we want to find this probability P(+) and for this case we can use the Bayes total rule and we can do this:

And if we replace we got:

Part bWe want to find this probability and using the bayes rule we have:

We can find the numerator from:

And then if we replace we got:

Part cWe want to find this probability and using the bayes rule we have:

We can find the numerator from:

And then if we replace we got: