A student believes that a certain 6-sided number cube, with the numbers 1 to 6, is unfair and is more likely to land with a 6 facing up. The student rolls the cube 100 times and lands with 6 facing up 20 times. Which hypotheses would test the student’s claim?

Suppose you are making a six faces dice. With each of the six faces, you need to put a number 1 to 6 on the faces so that each number is on a distant face. How many different dice can you make? (two dices are considered different if it is impossible to rotate the cube to match one another)

This is one question, but I couldn't fit it all in one photo so I attached two photos.

OSM HTAM MATH 1420 11. A roulette wheel has 38 slots around the rim. The first 36 slots are numbered from 1 to 36. Half of these 36 slots are red, and the other half are black. The remaining 2 slots are numbered 0 and 00 and are green. As the roulette wheel is spun in one direction, a small ivory ball is rolled along the rim in the opposite direction. The ball has an equally likely chance of falling into any one of the 38 slots. Find each of the following: a. The probability that the ball lands in a black slot. b. The probability that the ball lands on 0 or 00. C. The probability that the ball does not land on a number from 1 through 12 d. The probability that the ball lands on an odd number or on a green slot