2025 NYJC P2 Q6

Two fair six-sided dice are thrown. Events \(A\), \(B\) and \(C\) are defined as follows.

\(A\): sum of the two scores is odd
\(B\): at least one of the two scores is greater than \(4\)
\(C\): the two scores are equal

1. Find, giving your reasons clearly in each case, which pair of the events are
   1. mutually exclusive,[1]
   2. independent.[3]
2. Find \(\mathrm{P}(C \mid B)\).[2]