Explanation
Given Information
We are given a set of events E1,E2,…,En defined on a sample space S with the following conditions:
-
Ei∩Ej=∅ for all i=j (The events are Mutually Exclusive).
-
⋃i=1nEi=S (The events are Exhaustive).
-
P(E_i) > 0 for all i=1,2,…,n (Each event has a non-zero probability).
Concept
In probability theory, when a collection of events satisfies these three specific criteria, they fulfill the definition of a Partition of a Sample Space.
Explanation
-
Condition (i): This ensures there is no overlap between any two distinct events. If one event occurs, none of the others can occur simultaneously.
-
Condition (ii): This ensures that at least one of these events must occur during an experiment, as they cover the entire space S.
-
Condition (iii): This is a technical requirement to ensure that each "slice" of the partition actually exists and can be used as a condition for other probabilities (like in Bayes' Theorem).
Final Answer
The events E1,E2,…,En constitute a Partition of the Sample Space S. They are commonly referred to as a set of Mutually Exclusive and Exhaustive events.
