A hobby shop sells an eight-faced die whose faces carry the numbers 1, 1, 2, 4, 4, 4, 8 and 8. All eight faces are equally likely. The die is rolled once. What is the probability that the number on top is a perfect square?

Perfect squares among 1, 1, 2, 4, 4, 4, 8, 8 are the two 1s and the three 4s, so 5 faces out of 8 and $P=\frac{5}{8}.\frac{3}{8}$ counts only the 4s and forgets that $1=1\times 1$ is a perfect square; $\frac{7}{8}$ wrongly counts 8 as a square; $\frac{1}{2}$ treats the four different values 1, 2, 4, 8 as the outcomes instead of the eight faces.