Start from scratch. Let G denote the event : "the person has a glaucoma"
You're looking for the probability : , that is the probability that the person has a glaucoma given that his eyes' measurement is a.
Now what is given in the text ?
It means that if you pick someone who has a glaucoma, X will follow that normal distribution, which we'll denote as you did :For persons who have glaucoma measurements of eye pressure X will have normally distributed X with a mean of 25 and a variance of 1.
Once again, this is a conditional probability :
Similarly, we get :For persons whithout glaucoma the pressure X is normally distributed with a mean of 20 and a variance of 1
, where denotes the event "the person doesn't have a glaucoma". And we indeed have
Now look at this formula : Bayes' theorem - Wikipedia, the free encyclopedia (derived from Bayes' theorem)
From this, we can write :
Which is :
So you were correct.
Does it look clear to you ?