A regular tetrahedron is a triangular pyramid with 4 equilateral faces. Han has a box of regular tetrahedrons with each of the 4 vertices marked with one of the numbers 1, 2, 3, and 4. He rolls one tetrahedron and makes note of the number on the vertex that points up. After rolling this regular tetrahedron 10 times, he notices that the number 1 appears 5 times.

Han suspects that this tetrahedron is weighted in some way to make 1 appear more often than the other numbers. Using another regular tetrahedron from the box that he has confirmed is fair (all of the numbers tend to be rolled with equal frequency), explain a process Han could use to gather evidence to show whether this tetrahedron is also fair.

A spinner is divided into 3 equal sections labeled A, B, and C.

1. After spinning 30 times, how many times would you expect the spinner to land on C? Explain your reasoning.
2. After spinning the spinner 30 times, the frequency of the outcomes is the following: A 9 times, B 8 times, C 13 times. Is the number of times the spinner landed on C reasonable based on your expectations? Explain your reasoning.
3. The spinner is spun 3,000 times. Give an example of a number of spins that result in C that would be possible but unusual. Explain your reasoning.