Suppose that we have a very special die which has exactly \(k\) faces where \(k\) is prime. The faces are numbered \(1,\dots,k\). We throw the die once and see which number comes up.

1. What would be an appropriate outcome space and probability measure for this random experiment ?
2. Suppose that the events \(A\) and \(B\) are independent. Show that \(\mathbf{P}(A)\) or \(\mathbf{P}(B)\) is always either 0 or 1. Or in other wards \(A\) or \(B\) is always either the full space or the empty set.

[ from Meester, ex 1.7.32]