Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 2 / 1 / Solution

Ignoring factors that do not depend on the parameters, the product of the two binomial likelihoods isIncluding the sampling constants multiplies this by $\left(\genfrac{}{}{0ex}{}{200}{120}\right)\left(\genfrac{}{}{0ex}{}{220}{110}\right)$.