Two events A and B defined on a sample space S are said to be collectively exhaustive if:
A)A ∩ B = ∅
B)A ∪ B = ∅
C)A ∩ B = S
D)A ∪ B = S

Question

Quizplus · Accepted Answer

The events A and B are collectively exhaustive if their union A ∪ B covers the entire sample space S, meaning that any outcome in S belongs to either A or B or both. Therefore, the correct choice is D. Choices A and B are contradicting as A ∩ B cannot be empty if A ∪ B is empty. Choice C is incorrect as the intersection A ∩ B may cover only a part of the sample space, not necessarily all of it.

Two Events a and B Defined on a Sample Space