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We have 36 possible elementary events.

I want to know what is the probability that I rolled an even number, given that I rolled both same dice.

So my event A={<1,1>, <2,2>, <3,3>, <4,4>, <5,5>, <6,6>}

My event B={<2,2>, <4,4>,<6,6>}

Conditional probability is,

P(B|A)=P(A and B)/P(A) = 0.5

I mean its intuitive, if I rolled the both dice with the same number I have 50:50 percent chance that I got an even number.

Now are these events independent? My gut is telling me that they aren't and math is confirming that.

This is an example I worked out myself, to try to explain this to myself, so I just need somebody to confirm it.