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We roll two dice once. Let X denote the number of 1’s and Y the number of 6’s obtained. Are X and Y independent?

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Don't think so... if $X=2$, can $Y$ be anything other than $0$? –  Arturo Magidin Apr 28 '12 at 6:19
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up vote 4 down vote accepted

Is $P((X=1) \cap (Y=2))=P(X=1)P(Y=2)$?

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No, thanks for the example –  Daniela del Carmen Apr 29 '12 at 2:03
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