Learn by Doing – Tests for Independent Events

Published: January 29th, 2013

Category: Activity 1: Learn By Doing

It is vital that a certain document reach its destination within one day. To maximize the chances of on-time delivery, two copies of the document are sent using two services, service A and service B, and the following probability table summarizes the chances of on-time delivery:


Are the delivery times of the two services independent? In other words, are the events A and B independent? Common sense would say that there will be some degree of dependence between A and B, since the reasons that would cause one service to be delayed (like bad weather, airport delays, etc), would most likely also affect the other service, and cause it to be delayed too. Let’s review the four possible methods that we can use to check whether events A and B are independent:

Two events A and B are independent if any one of the following hold:

  • P(B | A) = P(B)
  • P(A | B) = P(A)
  • P(B | A) = P(B | not A)
  •  P(A and B) = P(A) * P(B)


This document is linked from Conditional Probability and Independence.