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Blood types refer to the classification of blood based on the presence or absence of certain antigens on the surface of red blood cells. There are four main types: A, B, AB, and O. Each type can be positive or negative, depending on the presence of the Rh factor. In the context of the exercise, type AB blood is significant because an emergency call specifically requested this type. Individuals with AB blood have both A and B antigens, making them universal plasma donors.

The problem involved differentiating between individuals with and without type AB blood. Understanding blood types is crucial for various reasons:

• They determine compatibility in blood transfusions and organ transplants.
• Knowledge of blood types helps in emergency situations where specific types might be urgently needed.
• Blood types also have implications in population studies and genetic research.

Recognizing the properties and significance of different blood types helps in crafting solutions to statistical problems like the one presented.

Random sampling is a method used to select individuals from a larger pool in such a way that every possible sample has an equal chance of being chosen. In the exercise, the concept of random sampling is crucial as the blood samples are taken one by one in random order.

This randomness ensures that:

• There is no bias in the selection process, meaning each individual has an equal chance of being selected first, second, or third.
• It creates the foundation for calculating probabilities, as seen by how the scenarios for picking AB blood types are structured.
• Random sampling plays a vital role in obtaining a representative subset from a population, aiding in accuracy and validity of statistical conclusions.

Employing random sampling in this exercise helps determine the probabilistic outcomes and their respective distributions accurately by considering every possible order of sampling.

Discrete random variables take on distinct and separate values, often whole numbers derived from counting. In the context of the exercise, the discrete random variable is represented by the number of samples taken (\( x \)) to obtain an AB blood type. Here, \( x \) can be 1, 2, or 3, each representing scenarios with corresponding probabilities.

Discrete random variables are important because:

• They allow us to evaluate and calculate probabilities for specific outcomes, as demonstrated in the given exercise.
• Outcomes are defined in terms of countable, distinct events, thus lending clarity to statistical interpretations.
• Understanding these variables offers insight into scenarios with finite or countable datasets, common in real-world problems.

Grasping how discrete random variables work gives us the ability to model and solve problems involving probability distributions, as demonstrated through the calculation of the probability for each potential value of \( x \) in the exercise.