Suppose that a person's birthday is a uniformly random choice from the 365 days of a year (leap years are ignored), and one person'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?

Question

Mathematics

Trevin Beard

5 June, 20:34

Suppose that a person's birthday is a uniformly random choice from the 365 days of a year (leap years are ignored), and one person'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?

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Paula Hayden · Answer 1

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.