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In probability theory, a sample space is the set of all possible outcomes of a probability experiment. In our tea-tasting experiment, we are dealing with the rankings of three tea brands labeled A, B, and C. Since the taster is tasked with ranking them, we must consider every possible order in which the taster might prefer them.
These possible rankings represent the different outcomes, termed 'simple events', that exist in our sample space.

• A > B > C
• A > C > B
• B > A > C
• B > C > A
• C > A > B
• C > B > A

This accounts for a total of 6 different outcomes, or simple events, that define our sample space in this experiment. Each event corresponds to a unique ranking arrangement of the three teas.

Ranking in this context refers to ordering the three tea brands from most desirable to least desirable. The person conducting the taste test does not know which brand corresponds to which label (A, B, or C), eliminating any bias.
The concept of ranking is based on the assumption that the taster relies solely on their taste preference during the test. This ensures the authenticity of the results. Since there are three tea brands, each taster has 3 choices for the first position, then 2 remaining choices for the second position, and only 1 choice left for the third position.
This calculation, known as a factorial, is written as 3!, which is equal to 6. These 6 unique rankings form the total number of possible ways to rank the teas in this experiment.

A simple event is one specific outcome or occurrence from the sample space. It involves no further breakdown and cannot be divided into smaller parts. For the tea ranking exercise, each simple event is a specific sequence or order in which the teas are ranked.
To illustrate, consider the simple event A > B > C. Here, the taster ranks tea A as the most preferred, followed by B, and lastly C. Each ranking arrangement, like A > B > C or C > B > A, is a distinct simple event.
Understanding simple events is crucial as they serve as the basic building blocks to calculate probabilities in more complex scenarios. They help in analyzing how each specific outcome contributes to the overall probability experimentation in this case.

Equally likely outcomes mean that each outcome within the sample space has the same probability of occurring. In our experiment, it is assumed that the taster cannot tell the difference between the teas based on taste alone. This implies that the rankings are purely random, with no bias or preference affecting them.
Given this assumption, the 6 possible rankings are equally likely. Thus, each configuration has an equal chance of happening, with a probability of \(\frac{1}{6}\)because there are 6 possible outcomes.
Equally likely outcomes simplify calculations of probability, as each event carries the same weight or chance of occurring. This fairness is essential in applications requiring unbiased interpretations like surveys, unbiased random sampling, and probability evaluations.