Final answer:
To answer the question about the probability of a random variable falling between two values, information on the type of distribution is necessary. In independent events, we multiply individual probabilities, and for uniform distributions, all outcomes have equal likelihood. In continuous distributions, probabilities are calculated for ranges of values but not for single points. Thus, the correct option is A and B.
Step-by-step explanation:
The question pertains to finding the probability that a random variable falls between two values, which is a common problem in statistics, specifically under the subject of probability distributions. While the question does not specify the type of distribution, interpreting the problem and the provided keywords suggests it could relate to normal distributions or discrete random variables, such as binomial or uniform distributions.
For example, when dealing with independent events A and B, the probability of both events occurring simultaneously, P(A AND B), is found by multiplying their individual probabilities if the events are independent (P(A) * P(B)). In uniform probability distributions, each outcome within the defined range has an equal probability of occurring, while in normal distributions, probabilities are calculated based on the distance from the mean in terms of standard deviations.
To provide a definitive answer to the student's question, more information about the random variable's distribution is needed. For continuous distributions, the probability of the variable taking on any single value is 0, but probabilities for ranges of values can be calculated using the cumulative distribution function or z-scores if the distribution is normal.