Question #1
The probability that a student fails physics is 0.23. The probability that the student fails chemistry and physics is 0.17. Find the probability that the student fails chemistry given that he or she fails physics.

In this case, of conditional probability, let’s denote the students who failed physics as PH with a probability of 0.23. On the other hand, let us denote the student that failed chemistry and physics to be CP with a probability of 0.23. The question aims to find out the probability P, that the student fails chemistry given that he or she fails physics. This can be equated as P (PH) = 0.23 and P (CP) = 0.17.
Based on this background, the probability that the student fails chemistry given that he or she fails physics is
P (C/PH)= P (CnPH)/PH = 0.17/0.23 =0.739
The above calculation shows that the probability of a student failing chemistry given that he or she fails physics is 0.739.