Two events E and F are independent if and only if
P(EF) = P(E) P(F).
Here,
E = event that neither dice is a 1; P(E) = 25/36
(exclude all outcomes containing a 1)
F = event that both show the same number; P(F) = 1/6
EF = event that neither dice is a 1 and both show the same number; P(EF) = 5/36
(the outcomes: (2, 2), (3, 3), ... , (6, 6))
Since
the events E and F are dependent.
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