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please help me out here, i dont even know where to start with this question :(. Any guidelines anything at all that may give me an idea to answering the question will be greatly appreciated.

Please also suggest any book that covers this kind of problems.

Thanks.

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You have to proof if all the combinations of the events are independent.

pairwise comparision:

number of conditions: $n \choose 2$. That is the number of all combinations of two events from n events.

Then you have to prove $P(A_i \cap A_j \cap A_k)=P(A_i)\cdot P(A_j)\cdot P(A_k) \ \quad \forall i\neq j \neq k; i,j,k=1,..,,n$

number of condition.:$n \choose 3$

If you go on like this, you have $\sum_{k=2}^n {n \choose k}$ conditions for n events. This can be simplified by using the Binomial Theorem.

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  • $\begingroup$ so the expansion of the sum will be the number of conditions? i.e 2^n-n-1 ?? $\endgroup$
    – HappyFeet
    Aug 1, 2014 at 16:55
  • $\begingroup$ @Ozwurld That´s correct. $\endgroup$ Aug 1, 2014 at 16:58
  • $\begingroup$ Heres what i understand so far about this, please see link, could you please give me pointers on how to prove P(Ai∩Aj∩Ak)=P(Ai)⋅P(Aj)⋅P(Ak) ive been googling with no luck! $\endgroup$
    – HappyFeet
    Aug 2, 2014 at 20:05
  • $\begingroup$ @Ozwurld This is just one condition for indenpendency of 3 or more events. Whitout knowing something about the events $A_i$ you can´t check it. What you have written looks good. $\endgroup$ Aug 3, 2014 at 6:32

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