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

Question

please i want to prove this equestion is statistically independent

Answer 1

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)