My Math Forum Are these events independent?

 Probability and Statistics Basic Probability and Statistics Math Forum

 October 7th, 2019, 12:33 AM #1 Newbie   Joined: Oct 2019 From: Lo Posts: 1 Thanks: 1 Are these events independent? Hello everyone. Let us consider 3 events A,B,C such that: $$P((A \cap B )\cup C)=P(A)*P(B)*P(C)$$ Notice that the second term is a union and not an intersection. Are they independent? And what if the assumption was: $$P(A \cap( B \cup C))=P(A)*P(B)*P(C)$$? I know that the independence condition requires us to check whether the probability of the intersection of each pair factorizes plus the probability of the intersection of all of them factorizes as well. But I do not know how to prove that they are/they are not independent Thank you. Thanks from idontknow
October 7th, 2019, 07:30 AM   #2
Senior Member

Joined: Mar 2015
From: Universe 2.71828i3.14159

Posts: 132
Thanks: 49

Math Focus: Area of Circle
Quote:
 Originally Posted by Patt Hello everyone. $$P((A \cap B )\cup C)=P(A)*P(B)*P(C)$$
$$P((A \cap B )\cup C) = [P(A) \times P(B)] + P(C) - [P(A) \times P(B) \times P(C)]$$

 Tags events, independent

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post beesee Probability and Statistics 2 June 9th, 2015 01:52 PM Abstract3000 Algebra 1 February 16th, 2014 12:25 PM Keroro Algebra 1 June 6th, 2012 08:17 AM daivinhtran Algebra 1 April 10th, 2011 01:07 PM Siria Advanced Statistics 4 July 5th, 2009 09:21 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top