an unbiased die rolled n times. what is the probability that the product of the scores is an even number

Answer 1

As long as one of the numbers is even, the product will be even
So to have an odd product, all of the factors must be odd
to have n consecutive odds is (1/2)^n

So to have an even would be
1 - (1/2)^n

e.g.
suppose we roll it three times, n = 3
according to my formula,
prob(even) = 1 - (1/2)^3 = 7/8

cases:
EEE
EE0
EOE
OEE
E00
0E0
00E
000
The first 7 will all produce an even product
so Prob(even product) = 7/8