Question

If E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________

(a) P(E∩F) / P(F), provided P(F) ≠ 0

(b) P(E∩F) / P(F), provided P(F) = 0

(c) P(E∩F) / P(F)

(d) P(E∩F) / P(E)

I got this question during an internship interview.

This key question is from Conditional Probability in chapter Probability of Mathematics – Class 12

Answer 1

Right choice is (a) P(E∩F) / P(F), provided P(F) ≠ 0

To elaborate: E and F are two events associated with the same sample space of a random experiment.

The value of P (E|F) = (E∩F) / P(F), provided P(F) ≠ 0. We know that if P(F) = 0, then the value of P(E|F) will reach a value which is not defined hence it is wrong option. Also, P(E∩F) / P(F) and P(E∩F) / P(E) are wrong and do not equate to P(E|F).