Final answer:
The question addresses probability distributions and their applications to calculate event probabilities, including those that are mutually exclusive and independent. It also explains the characteristics and implications of the uniform distribution in the context of inclusive or exclusive endpoints. So, the correct answer is A.
Step-by-step explanation:
The question pertains to the concept of probability distributions in mathematics, particularly how events can be classified as mutually exclusive, independent, or neither, and how to compute various probabilities related to these events. Key formulas and principles of probability are applied to calculate probabilities such as P(C AND D), P(C OR D), and conditional probabilities like P(B|D). The uniform distribution is specifically mentioned, characterized by all outcomes being equally likely within a given range.
For discrete events, the probability that two events are mutually exclusive means that they cannot both occur at the same time-P(A AND C) in this case is zero. Independent events refer to situations where the occurrence of one event does not affect the probability of the other event occurring. Calculations for independent events involve the multiplication rule, where P(A AND B) is the product of P(A) and P(B) if events A and B are independent.
The uniform distribution is a type of continuous probability distribution that assumes every outcome in its range is equally likely. It is important to be clear about whether the data are inclusive or exclusive of endpoints when dealing with this distribution. Inclusion of endpoints can affect the calculation of probabilities.