Ive sort of advanced a little on this...

Since the two trials are independent, the total max log-likelihood is the sum of the two individual trials i.e.

Trial 1; max log-likelihood is

Trial 2; max log-likelihood is

Adding these together gives total max log-likelihood.

Is the max log-likelihood for each individual trial found by doing something like finding the derivative of the log-likelihood and setting it to 0? I'm mostly unsure as to where the binomial expression comes from...