# Probability in tests in genetics

Q. A certain gene is necessary for certain protein synthesis in human beings. A new kind of test can detect the gene in people who have the gene 99.9% of the time, and falsely detects the gene 10.3% of the time when a person does not carry the gene. 93% of the population carries the gene disease.

. What is the probability that a test result states the gene is detected?
. What is the probability the test is wrong?

I do not know how i would even attempt this question...any guidelines?

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Well, you might want to look into Bayes' Theorem (try Wikipedia).

An intuitive way to do it is to create a large population, and then figure out what happens to it.

So suppose there are 100,000 people. How many of them actually have the disease? Suppose we test them all. How many are correctly identified as having it? How many false positives are there? How many silent negatives are there? etc...

Okay! So would the probability that a rest result states the gene is detected be 0.936?

would work down to something like:

(99.9% x 93%) + (10.3% x 0.07%)

=0.93628 ??

Yes, that's right.

Okay sweet!

Okay what if it ask What is the probability the test is wrong...What would i do in that instance?

Well, take a stab at it yourself. You have all these tests (93.6% positive, the rest negative). How many of them are right?

I come up with 0.098, but i believe that is wrong. Other than that, I have no idea. Can you elaborate a little bit?

Categorize all the people into the following:

Has the gene/test says yes
Has the gene/test says no
No gene/test says yes
No gene/test says no

The Probability that the test is wrong would then equal 0.007

How'd you get that? It seems close but a little too low.

i have a page full of calculations. they keep changing everytime i try something new. 0.077 is what im getting now man any ideas?

Well let's see. Someone has the gene 93% of the time, and when they do it's reported that they have it 99.9% of the time. So out of 100k people, 930 would have the gene but the test would say no.

7% of people don't have the gene, and it's reported that they do 10.3% of the time. So out of 100k people, 7000 don't have the gene, and 721 get positive test results.

So summing those, we get that 1651 people would get wrong test results if everyone were tested, or about 1.65%.

awesome thanks