Consider two events E and F defined on the same sample space S. Answer the following questions related to these events.
a. (i) Define the probability of E given that F has already occurred.
b. (ii) Explain why the quantity you defined in part (i) is not meaningful when P(F)=0.
c. (iii) Clearly distinguish between P(E∩F) and P(E∣F) by citing any suitable example from everyday classroom situations (for instance, results of two different subjects in an examination).
d. (iv) A teacher notes that 70% of the students in a class passed Mathematics (event M), 60% passed Physics (event P) and 50% passed both subjects. Interpret, in words, the value of P(M∣P) for this class.