Two events E and F are independent if and only if
P(EF) = P(E) P(F).
Here,
E = event that the red die is a 1; P(E) = 1/6
F = event that the sum is even; P(F) = 1/2
EF = event that the red die is a 1 and the sum is even; P(EF) = 3/36
(since there are a total of 3 outcomes of this form: (1, 1), (1, 3), and (1, 5) )
Since
the events E and F are independent.
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