91Ó°ÊÓ

Disjoint events, also known as mutually exclusive events, are two events that cannot happen at the same time. In probability, identifying disjoint events can simplify calculations and help us understand real-world situations better. For two events to be disjoint, the occurrence of one event means the other cannot happen. This can be likened to a simple scenario of flipping a coin – the result can be either heads or tails, but not both simultaneously.

In this exercise, the probability events are defined in terms of obesity:

• Event \( A \) is when the chosen person is obese.
• Event \( B \) is when the person is overweight but not obese.

These conditions show that if a person belongs to event \( A \), they cannot belong to event \( B \), and vice versa. Thus, events \( A \) and \( B \) are disjoint, allowing us to use specific rules in probability, such as the Addition Rule for disjoint events.

The complement rule in probability is an efficient way of finding the probability of an event not occurring. When the total probability of all possible outcomes in a sample space is 1, we can calculate the probability of the complement of an event, which is simply everything that is not the event itself.

Mathematically, if we are considering an event \( A \), its complement, often denoted as \( A^c \), is defined as \[ P(A^c) = 1 - P(A) \] This rule helps us determine the likelihood of scenarios where certain conditions are not met.

In our exercise, event \( C \) is described as having a normal weight or less, meaning not being overweight or obese. Since \( C \) is the complement of "being overweight or obese," we apply the complement rule to find \( P(C) \, \), which is calculated from the probability of being either obese or just overweight: \( P(C) = 1 - P(A \text{ or } B) = 1 - 0.72 = 0.28 \).

Probability calculation is a fundamental concept used to predict how likely an event is to occur. The basis of calculating probabilities involves understanding the relationships between different events and applying appropriate formulas accordingly.

When dealing with disjoint events like \( A \) and \( B \) from the exercise, the calculation of the probability of either event occurring ("\( A \text{ or } B \)") is straightforward: we simply add the probabilities of each event occuring, because they cannot happen at the same time. \[ P(A \text{ or } B) = P(A) + P(B) \] For instance, \( P(A \text{ or } B) = 0.40 + 0.32 = 0.72 \).This approach simplifies calculations by considering that each event is independent of the other in terms of occurrence.

In probability, an event is defined as a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. Defining events clearly is crucial in solving probability problems, as it establishes the framework for analysis.

In this exercise, events are specifically defined within a broader context of health classification:

• \( A \): The person is obese.
• \( B \): The person is overweight but not obese.
• \( C \): The person has normal weight or less.

By defining these events, we can apply relevant probability rules and methods systematically. Understanding this well-structured approach helps students navigate more complex problems, ensuring clarity and correctness in evaluations.