Suppose that a person's birthday is a uniformly random choice from the 365 days of a year (leap years are ignored), and one pers
on's birthday is independent of the birthdays of other people. alex, betty and conlin are comparing birthdays. define these three events: a = {alex and betty have the same birthday} b = {betty and conlin have the same birthday} c = {conlin and alex have the same birthday} are these events independent ?
P ( A ∩ B ∩ C) = 1/365 P(A) = 1/365, P(B)= 1/365, P(C) = 365 If events A,B and C are independed then P (A ∩ B ∩ C) = P (A) P(B) P(C) must be true, From the probabilities we have 1/365≠ 1/365 * 1/365 * 1/365 Thus, events A,B, C are not independent.
