Sure, the actual difference in probability is minute, so it essentially has 0 predictive power.
That is, statistics also tells us that P(n>50 | first ball is red) ~= P(n>50) ~= P(n<50) ~= P(n<50 | first ball is red).
Of course, the problem statement is not realistic in the slightest because it gives you too much other (critical) information as well: you are told that n has a uniform probability distribution. In reality, you never know the probability distribution a priori (even when analyzing a die or coin, you can't be a priori certain it is fair). And the conclusion in this problem, even weak as it is, depends critically on knowing the probability distribution. Not only would the conclusion be different is n was not uniformly distributed between 1 and 100, but you can't even do a similar analysis over all possible probability distributions.
That is, statistics also tells us that P(n>50 | first ball is red) ~= P(n>50) ~= P(n<50) ~= P(n<50 | first ball is red).
Of course, the problem statement is not realistic in the slightest because it gives you too much other (critical) information as well: you are told that n has a uniform probability distribution. In reality, you never know the probability distribution a priori (even when analyzing a die or coin, you can't be a priori certain it is fair). And the conclusion in this problem, even weak as it is, depends critically on knowing the probability distribution. Not only would the conclusion be different is n was not uniformly distributed between 1 and 100, but you can't even do a similar analysis over all possible probability distributions.