Thread: find the probability

Hello. I am having problems with this prob question, thanks for your help:

G= guilty
P(G)= 2/3
I= innocent
P(I)= 1/3
The judge comes to know the result x of the test of DNA of the accused person. If guilty, the probability of x is 90%. If innocent is 5%.

Which condition on the probability of x, subject to the two events G and I has to be satisfied so that the final probability atributed by the judge to the innocence I is 100%.

the book says P(x|G)=0. Why? I can't get it. Thank you very much.

Originally Posted by 0123

Hello. I am having problems with this prob question, thanks for your help:

G= guilty
P(G)= 2/3
I= innocent
P(I)= 1/3
The judge comes to know the result x of the test of DNA of the accused person. If guilty, the probability of x is 90%. If innocent is 5%.

Which condition on the probability of x, subject to the two events G and I has to be satisfied so that the final probability atributed by the judge to the innocence I is 100%.

the book says P(x|G)=0. Why? I can't get it. Thank you very much.

Problem 1 is that you are already told that P(x|G)=0.9


Ignore that, P(I|x)+P(G|x)=1, so P(I|x)=1 implies P(G|x)=0, so

P(G|x) = P(x|G)P(G)/P(x)

P(x)=P(I)P(x|I) + P(G)P(x|G)

Now assume P(x) != 0, and that P(G) != 0, then P(G|x)=0 implies that
P(x|G)=0

RonL