From a set of n randomly chosen people, let Eij denote the event that persons i and j have the same birthday. Assume that each person is equally likely to have any of the 365 days of the year as his or her birthday. Find
(a) P(E3,4|E1,2);
(b) P(E1,3|E1,2);
(c) P(E2,3|E1,2 ∩ E1,3).
What can you conclude from your answers to parts (a) – (c) about the independence of the
events Eij?