Seven tosses of a fair coin are made one after another. What is the probability that heads come up more often than tails?

Seven is odd, so a tie is impossible and every outcome is a win either for heads or for tails. Turning every head into a tail and every tail into a head pairs the outcomes off exactly, matching each 'more heads' outcome with a 'more tails' one, so the two events must be equally likely and the answer is 1/2 without any counting. Counting confirms it: at least 4 heads happens in $C(7,4)+C(7,5)+C(7,6)+C(7,7)=35+21+7+1=64$ of the $2^7=128$ outcomes, and 64/128 = 1/2. The option 35/128 counts exactly four heads, 99/128 answers 'at least three heads', and 1/128 is all seven heads.