List all the ways the Heads and Tails can occur. This is the expansion of
The events with even Heads are those terms with H^(even power), in other words every other term.
You can verify that the sum of the even terms in the binomial is the same as the sum of the odd terms in the binomial by expanding (1-1)^491 = 0. Note that the (-1) keeps track of the even and odd terms.
So, yes, it is 50%.