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The Graduate Management Admission Test, commonly known as the GMAT, is an assessment that evaluates the essential skills needed for success in graduate business programs. This test is a pivotal element for prospective students aiming to enroll in institutions to pursue an MBA or other graduate-level management degrees. The GMAT is designed to assess various capabilities, including analytical writing, quantitative reasoning, verbal reasoning, and integrated reasoning.

Preparing for the GMAT is crucial, as it often forms a prerequisite for admission into many prestigious business schools worldwide. Courses and materials are available to help students improve their scores, and understanding the demographic of students attending these preparation courses can offer insights into the test's wide reach.

Probability in statistics helps us measure the likelihood of different kinds of outcomes. When dealing with a probability question about students in a GMAT preparation course, it is essential to accurately identify different student categories.

In our context, undergraduate students are split into two categories: those studying business and those in other fields. To find the total probability of a customer being an undergraduate, these probabilities are added. This is known as the Addition Rule because these categories do not overlap; a student cannot simultaneously be in both categories. Therefore, the probability that a selected customer is an undergraduate is the sum of the percentages of undergraduate business students (20%) and students in other fields (15%), totaling 35%.

The Addition Rule is a fundamental principle in probability that allows us to find the probability of either of two mutually exclusive events occurring. These events cannot happen at the same time. Hence, their probability is computed simply by adding their individual probabilities.

In practice, this rule means that to find the probability of selecting an undergraduate student from the course attendees, we add the probability of a student being a business undergraduate (20%) to the probability of a student being from another field of study (15%). Thus, by applying the Addition Rule, we determine that there is a 35% chance of randomly selecting an undergraduate student.

The Complement Rule is a simple yet powerful concept in probability. This rule helps us determine the likelihood of an event not happening by focusing on its complement—the event that represents all outcomes that are not in the event itself. If the probability of an event occurring is known, we can find the probability of it not occurring by subtracting this from 1.

For example, if we wish to determine the probability that a customer is not an undergraduate business student, we identify the complement of the event where a customer is an undergraduate business student (which has a probability of 20%). The Complement Rule tells us that the probability of not being a business undergraduate is 1 minus this value: \[1 - 0.20 = 0.80\] resulting in an 80% probability.