if 1:1000 of people is sick. the probability to be false positive is 0.07. if a person is sick there

fabios3

fabios3

Answered question

2022-06-08

if 1:1000 of people is sick. the probability to be false positive is 0.07. if a person is sick there is not chance the test for the disease is wrong. If someone random is got a positive result, what are the chances he's actually sick?
I got 1.5% and wanted to check because I feel it should be more since the diagnose is never wrong. I took 1/1000 and divided it by 0.07+1/1000 and multiplied by 100 to get the percent.

Answer & Explanation

Korotnokby

Korotnokby

Beginner2022-06-09Added 19 answers

Your calculations are not quite correct.
P ( sick | positive test ) = P ( positive test | sick ) P ( sick ) P ( positive test )
We know P ( positive test | sick ) = 1 and P ( sick ) = 1 / 1000. As for the denominator,
P ( positive test ) = P ( positive test | sick ) P ( sick ) + P ( positive test | not sick ) P ( not sick )
We know P ( positive test | sick ) P ( sick ) = P ( sick ) = 1 / 1000 and P ( positive test | not sick ) P ( not sick ) = ( 7 / 100 ) ( 999 / 1000 ). So it should be
P ( sick | positive test ) = 0.001 0.001 + 0.07 0.999 0.0141
or 1.41 %
But your question remains: this is surprisingly low, right?! The reason is that very few people have the disease! If 1000 people get the test, on average only one will have the disease, but about 70 .07 999 healthy people will test positive.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?