You don't need to think in terms of information to get the right answer, you just need to be careful of the setup. You can easily apply frequentist probability

You don't need to think in terms of information to get the right answer, you just need to be careful of the setup. You can easily apply frequentist probability reasoning and still get the right answer. You have to start from P(n > 50 | first pull is a red ball), and compute P(second ball red | first ball red) based on that. Basically the mistake is computing the frequency over 100 balls, instead of computing it over the 100 possible values of n multiplied by the 100 balls.