I roll a dice twice. Let's say that A = odd number on first, B = even number on second, C = sum is odd.

Now, I need to calculate P(A), P(B), P(C) and P(A cut B).

Let's start, I think these three events are independent on each other.

And thus these are ( I think ) relevant,

P(A cut B) = P(A) P(B),

P(A cut B) = P(A) P(C),

P(B cut C) = P(B) P(C),

P(A cut B cut C) = P(A) (B) P(C)

cut means intersection, as you know.

Because there are numbers 1-6,

A = 1/6, B = 1/6, C = 1/6

And therefore

P(A) = P(A) P(B) = 1/6 * 1/6 = 1/36

P(B) = P(A) P(C) = 1/6 * 1/6 = 1/36

P(C) = P(B) P(C) = 1/6 * 1/6 = 1/36

P(A cut B) = P(A cut B) = P(A cut C) = P(B cut C) = (1/6)^3 = 1/216

Maybe this is not this easy? I don't know have I done this right?