Question

The table below dislays results from experiments with polygraph instruments. Find P(subject lied | negative test result}. Comapre this result with the probability of selecting a subject with a negative test result., given that the subject lied. Are P(subject lied | negative test result) and P(negative test result | subject lied) equal?

No (Did not lie) Yes (lied)
Positive test results 16 42
Negative test results 33 12

Answer 1

That bar | indicates 'given' the result after the bar |.

So P(subject lied|negative test result) means you go to negative test result row and find the fraction who lied out of that. The positive test result row doesn't matter as we are told the subject came from the negative test result to start with.
This is 12 out of 45 = 4/15 subjects who had negative test results.

for the other one focus on the subject lied column only and take the fraction of those with negative test result.