please i want to prove this equestion is statistically independent

## prove p(A,B,C)=p(A)p(B)p(C)

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# 1 Answer

OK, here we go!

think about the basics: AB=A*B Right?... good

Next, A(B) = A*B Still with me?

OK, now we will add some things in. ... ABC = A*B*C

and lastly A(B+C) = A (B+C) = A(B)+A(C)

So, If P(A+B+C) = P(A)+P(B)+P(C) we should get the same answer no matter how we do the problem.

If we do P(A+B+C) then 2(2+2+2) = 2(6) = 12. So our answer is 12

if we do P(A)+P(B)+P(C) then 2(2)+2(2)+2(2) = 4+4+4 = 12.

The answer is the same so 2(2+2+2) = 2(2)+2(2)+2(2)