Independence of 3 Events

Posted on February 28, 2015 by Sumant Sumant

We all know the case for independence of two events which is P(E_1 \cap E_2) = P(E_1) \cdot P(E_2). Now the questions is what are the conditions necessary for three events to be independent. Is it P(E_1\cap E_2\cap E_3)=P(E_1)\cdot P(E_2)\cdot P(E_3) ? or there is more to it. The answer is it should also satisfy the mutual independence of the three events too. Here is an example which illustrates that where we have mutual independence among the three events, however the total independence is not there.

Suppose we toss two coins and there are following three events. E_1 =\text{The first coin has a head }

E_2 =\text{The 2nd coin has a head }

E_3 =\text{Both the coins have different face }. Are these three events independent ?

Ind3Events

About Sumant Sumant

I love Math and I am always looking forward to collaborate with fellow learners. If you need help learning math then please do contact me.
This entry was posted in Probability and tagged . Bookmark the permalink.

Leave a comment