Determining whether A, B and C are independent.

Question

Toss two fair dice. Let $A$ be the event the first die comes up odd, and let $B$ be the event the second die comes up odd. Let $C$ be the event that the sum of the values which come up is odd. Are $A,B$ and $C$ independent? Justify!

$$P(A) = P(B) = P(C) = \frac{1}{2}$$

But how do you determine they are independent?

I don't understand how $P(A\cap B\cap C) = 0$.

Answer 1

HINT

If you know $A$ and $B$ can you determine $C$? If you express that in the formal definition of effecting the probability distributions, you will see what you need.

Answer 2

$A\cap B\cap C$ is the event that both dice give an odd number and that (nevertheless) the sum of these results is also odd.

How likely is that to happen?...