Final answer:
The question explores the properties of a fair die, such as equal probability of landing on any face and the sum of opposite faces being seven, and contrasts this with the properties of a biased die, which does not have equal probabilities for each face.
Step-by-step explanation:
The question pertains to the concept of probability and the characteristics of a fair and biased die in the context of theoretical and experimental probabilities. When discussing a novelty die, statement a) suggests that each face should have an equal probability of landing face up, which follows the assumption of a fair die.
Statement b) asserts that the sum of opposite faces is 7, a common feature in standard dice. However, statements c) and d) indicate that this particular die is biased and that not all faces have the same chance of landing face up, which contradicts the assumption of a fair die.
For a fair six-sided die, the probability of rolling any given number is exactly 1/6, since there are six possible outcomes and each is assumed to be equally likely. If the die is biased, as the claim suggests, certain numbers will have a higher likelihood of being rolled than others.
As we consider larger numbers of trials, like rolling a die many times, the long-term relative frequency of obtaining a specific result approaches the theoretical probability. However, for a biased die, the probability distribution would not be uniform.