The probability that "any one" die is even is, of course, 3/6= 1/3. But "any one" does NOT mean "one or more". You meant "at least one".
The opposite of "at least one" is "none". The probability that any one die is "not even", i.e. odd, is also 3/6= 1/2. The probability that none of four dice is even is \(\displaystyle \left(\frac{1}{2}\right)^4= \frac{1}{16}\) so the probability of "at least one even die" is \(\displaystyle 1- \frac{1}{16}= \frac{15}{16}\).
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