A wooden cube used in a village board game has its six faces marked 2, 3, 5, 5, 7 and 9 instead of 1 to 6. The cube is rolled once. What is the probability that the number on the top face is a prime number?

The six faces are equally likely. Of the numbers 2, 3, 5, 5, 7, 9 the primes are 2, 3, 5, 5 and 7 - that is 5 faces $(9=3\times 3$ is not prime). $P=\frac{5}{6}.\frac{4}{5}$ counts the five DIFFERENT numbers 2, 3, 5, 7, 9 as the outcomes, but the two 5 faces are separate outcomes; $\frac{2}{3}$ and $\frac{1}{2}$ come from miscounting the prime faces.