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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 ?

Respuesta :

zrh2sfo
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.

lhmarianateixeira

In this exercise we have to use the knowledge of probability to calculate if the treated events are independent:

The  events A,B, C are not independent.

Using the information given in the text, we can identify that:

  • P ( A ∩ B ∩ C) = 1/365
  • P(A) = 1/365
  • P(B)= 1/365
  • P(C) = 365

Using the probability formula we find that:

P (A ∩ B ∩ C) = P (A) P(B) P(C)  

1/365≠ 1/365 * 1/365 * 1/365

See more about probability at brainly.com/question/795909

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