# Pairwise independence of three events does not imply their mutual independence.How? [duplicate]

I am acquinted with the independent event derived from the the conditional probability.But In my book I read that mutual independence always imply pairwise independence but the converse is not always true.But I find difficulty when I was trying to find out an example to understand the matter well.Please give a suitable example which will meet my purpose.Thank you in advance.

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Let $A,B,C$ be random coin flips such that there are an even number of heads. Then they are pairwise independent but not mutually independent. I leave it to you to figure out why. =)
• @ArnabChattopadhyay: In other words, choose uniformly randomly from $\{(0,0,0),(0,1,1),(1,0,1),(1,1,0)\}$. Pairwise each possible combination is equally likely, but together only four of eight are possible. If it answers your question, you should mark it as accepted by clicking on the tick. If not, you can wait for more answers. – user21820 Oct 18 '15 at 0:46