Two friends, A and B, are tossing a fair coin together. Each of the first three coin tosses yields a "head", and they're about to toss it for a fourth time. A says the probability that the next coin toss yields a head is $0.5$. B says that since the probability that four consecutive coin tosses all turn up heads is $.0625$, the probability that the next toss yields a head should be $0.0625$ given the prior three heads.

---

I know intuitively that B is wrong and A is right, but can someone provide a mathematical explanation of why? Also, does Bayes' Theorem have any relevance here?