(a) Define the term “independent events” in the context of probability. (b) Prove…
MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability
Problem
(a) Define the term “independent events” in the context of probability.
(b) Prove that if two events E and F are independent and P(F)=0, then P(E∣F)=P(E).
(c) Three events A,B and C are said to be pairwise independent if every pair of them is independent, while they are said to be mutually independent if P(A∩B∩C)=P(A)P(B)P(C) in addition to pairwise independence. Explain, with the help of a suitable example, how a set of events can be pairwise independent but not mutually independent.