Complement from chained rule There is a probability problem like this:
There are three consecutive exams: programming exam, essay, and interview. To get the job, a student has to pass those three exams. The probability of passing a programming exam is 0.6. If it passes the programming exam, it passes the essay test with probability 0.7. If it passes the first two exams, it passes the third exam with probability 0.8. 
If we know a student didn't get the job, what is the probability it failed the essay exam?
Using chain rule, I get:
P(pass programming, pass essay, pass interview) =  P(pass interview | pass essay and programming) x P(pass essay | programming) x P(pass programming)

and then I find:
P(failed essay | pass programming) = 1 - P(pass essay | pass programming)
P(failed essay) = P(failed essay | pass programming) x P(pass programming)

However, I am confused on how to get P(failed essay | didn't get the job) from there.
Do I miss something?

Only 60% make it through the programming hurdle.  Of those 30% fail the essay and 0.7*0.2=14% pass the essay but fail the interview.  So 30/42 = 5/7 pass the programming exam but fail the essay. 
