b) In a large city, 8% of the inhabitants have contracted a particular disease. A test for this disease is positive in 80% of people who have the disease and is negative in 80% of people who do not have the disease. What is the probability that a person for whom the test result is positive has the disease?
The Answer to the Question
is below this banner.
Can't find a solution anywhere?
NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?
Get the Answers Now!You will get a detailed answer to your question or assignment in the shortest time possible.
Here's the Solution to this Question
We shall denote by and the following events:
Event : A person has a disease;
Event : A test for a person is positive;
The aim is to find a conditional probability . Namely, we have (https://en.wikipedia.org/wiki/Conditional_probability):
By direct computations we have:
In order to compute we use the law of total probability. Namely, we have:
Thus, we receive:
(it is rounded to 4 decimal places)
Answer: 0.2581 (it is rounded to 4 decimal places)