since you did not specify any other influencing factors or criteria, we have to assume that the probabilty among voters to have actually voted (valid vote) if the same as having put an invalid vote.
that is how I understand your problem text. but it could be that your skipped more information.
just to confirm, this is the problem text you put here :
"find the probability that among 1030 randomly selected voters, at least 771 did vote"
so, with that understanding, it is like tossing a coin : head or tails, voting (valid vote) or not voting (invalid vote).
the probabilty for such a single event is 1/2 or 0.5.
now, the probability to have exactly 771 "heads" is
(1/2)⁷⁷¹ × (1/2)²⁵⁹ = (1/2)¹⁰³⁰
771 times heads (votes), and 259 times tails (no votes).
this might surprise only at first glance, as having 771 heads is exactly only one of the 1030 different results we can get.
but now comes the trick : there are
C(1030, 771) = 5.197292284×10²⁵⁰
possibilities (combinations) to "pick" 771 out of 1030. and they all have the same single probabilty.
so, the probability to get exactly 771 heads (or votes) is
(1/2)¹⁰³⁰ × 5.197292284×10²⁵⁰ = 4.517327811×10^-060
the probability of getting at least 771 heads (votes) is the sum of all probabilities for getting 771, 772, 773, 774, 775, 776, ..., 1029, 1030 heads (votes).
that is
(1/2)¹⁰³⁰ × (C(1030, 771) + C(1030, 772) ... C(1030, 1030))
that requires the help of some calculator tool like Excel.
that sum (probability of having at least 771 votes) is
6.78917 × 10^-60