Thread: no clue how to do this question

1. no clue how to do this question

"The probability that any given person has a certain gene is 0.8 percent. Among people who have this gene, 80% test positively for it. Among people who do not have this gene, 5 percent test positively for it. What is the probability that a person who tested positively for the gene actually has the gene?"

How do I go about solving this? Or rather how would I go about setting up the appropriate equations?

2. Re: no clue how to do this question

Have you learned about Bayes' theorem?

3. Re: no clue how to do this question

I have heard of it and I tried to use it here but I'm not doing it right.

the probability of having the gene is P(G) = 0.008,

the probability of having a positive test given that you have the gene P(Pos|G)= 0.8

the probability having a false positive P(Pos|Gbar) where Gbar means you dont have the gene = 0.05

and I want to find the probability of having the gene if you tested positive for it P(G|Pos)

I can deconstruct any P(B|A) as P(B intersect A)/P(A) but in the case of testing positive for a gene what does P(Pos intersect G) mean? P(Pos|G) means 'probability of testing positive given that you have the gene" but P(Pos intersect G) means 'probability of testing positive AND having the gene' ...are these two the same in this case?

4. Re: no clue how to do this question

In general we can write:

5. Re: no clue how to do this question

i found Bay's theorem online and used that to answer the question. Thanks!

http://en.wikipedia.org/wiki/Bayes'_theorem

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