Probability

To define the event where the student passed only the statistics exam, we need to consider the intersection and complement of the given events A and B. Let's denote the event "The student passed only the statistics exam" as \( E \). Given: - Event \( A \): Passing the statistics exam. - Event \( B \): Passing the economics exam. We want to express \( E \) using \( A \), \( B \), and the operations of intersection, union, and complement. The event \( E \) occurs if the student passes the statistics exam and does not pass the economics exam. In terms of set operations, this can be expressed as the student being in set \( A \) but not in set \( B \). Mathematically, this is the intersection of \( A \) with the complement of \( B \), which is denoted as \( A \cap B' \). Therefore, the event "The student passed only the statistics exam" can be defined as: \[ E = A \cap B' \] This expression captures the idea that for the student to have passed only the statistics exam, they must be included in the set of students who passed statistics (event \( A \)) and simultaneously excluded from the set of students who passed economics (the complement of event \( B \), denoted as \( B' \)).

Math

A student takes two exams in a semester: one in economics and one in statistics. We define the following events: A - Passing the statistics exam. B - Passing the economics exam. Using only the intersection of events, union of events and complementary events; define the following event. The student passed only the statistics exam.

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