independence problem

[bour1992]

A server sends 3 digits (0 and 1) to a computer. The probability of sending 0 is p.
I have to check under which conditions the events:

A={at least 2 of 3 digits is 0}
B={all the digits are the same}

are independent.

I thought that they will be independent if the first 2 digits are different with each other.
e.g (0,1,0) or (1,0,0)

But i am not sure for that answer.
Can you tell me your ideas?

[mXSCNT]

If they are independent then P(AB) = P(A) P(B).
So to solve:
1. Determine a formula for P(AB) as a function of p
2. Determine a formula for P(A) P(B) as a function of p
3. Set them equal, and solve for p

[bour1992]

thank you mXSCNT for your help.

So after calculations I found that p=1 or p=1/2.
Can you confirm that this is the right answer?