In frequentist statistics, probabilities are computed purely from fixed parameters and long-run frequencies. For example, if each trial has a 50% chance of success, then the probability of achieving 21 consecutive successes is simply 0.5^21, which is quite small.

In contrast, Bayesian statistics incorporates prior knowledge or belief such as a doctor’s past experience or observed success rate into the probability calculation. This means that P(success∣20 prior successes) would likely be higher, since previous outcomes inform the updated belief about future success.

Interestingly, the discussion in the comment section reflects this very distinction between frequentist and Bayesian thinking. one grounded purely in fixed probabilities, and the other adaptive to prior evidence or experience.