Problem on bayes'

Bayes' theorem

You are doctor examining a middle-aged man who complains of lower back pain.

You know that
25% of men in the age group of your patient suffer from lower back pain.

There are various causes of lower back pain; one of them is chronic inflammation of
the kidneys. This is not a very common disease: it affects only 4% of men in the age
group that you are considering. Among those who suffer from chronic inflammation of the
kidneys, 85% complain of lower back pain.
What is the probability that your patient has chronic inflammation of the kidneys?

Sol below

Let's take 'K' for  kidney inflammation &
'L' for lower back pain

 P(L)=25/100.   P(K) = 4/100

P(L|I)= 85
             ------
              100

Using Bayes' formula


P(I|L)= P(L|I)P(K)
               -----------------
                  P(L)
       
          [ (85/100)(4/100)]
       = --------------------------   =0.136
                (25/100)