Hi...Can you plz check if my proof is correct?(adsbygoogle = window.adsbygoogle || []).push({});

Exercise:

A1,A2,.....An are independently events.

Prove that :

P(A1[union]A2[union]...[union]An) = 1-Πi[element-of]I(1-P(Ai))

note for this (Πi[element-of]I(1-P(Ai))

I={1,2,....n)

P([intersect]Ai)= Π P(Ai)

for 3 events A1,A2,A3

means: P(A1[intersect]A2)=P(A1)*P(A2)

P(A2[intersect]A3)=P(A2)*P(A3)

P(A2[intersect]A3)=P(A2)*P(A3)

P(A1[intersect]A2[intersect]A3)=P(A1)* P(A2) * P(A3)

Now my proof:

We know that P([intersect]Ai)= Π P(Ai)

if A1,A2,...,An are independent then and the complements

are independent

P([intersect]Ai)complement = Π P(Aicomplement)

P([union](Ai compl) ) = Π(1-P(Ai))

1-P([union]Ai)= Π(1-P(Ai))

-P([union]Ai)=-1+Π(1-P(Ai))

Finally ... we got our proof

P([union]Ai)=1-Πi[element-of]I(1-P(Ai))

Is it correct?

And one more....

but i dont know how to prove this:

A,B,C are independent

We must prove that A and B[union]C are independent too

...?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Probabilities and independence

**Physics Forums | Science Articles, Homework Help, Discussion**