Under which values of p and q, are the events A and B mutually exclusive? (Check all that apply.)

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BlackTom AI · Accepted Answer

Question restatement: Under which values of p and q are the events A and B mutually exclusive? (Check all that apply.)

Answer options:
- p=0 and q=0
- p=1 and q=0.5
- p=0.5 and q=0.5

Analysis of each option:
Option 1: p=0 and q=0
- In this case, both events A and B have probability zero of occurring. If neither A nor B can occur, their intersection A ∩ B is certainly empty, which satisfies mutual exclusivity (P(A ∩ B) = 0). This option is consistent with the definition of mutually exclusive events for the given scenario and aligns with the provided correct answer.

Option 2: p=1 and q=0.5
- Here, P(A) = 1 means A occurs in every trial. If A occurs with probability 1, then A ∩ B would occur whenever B occurs, giving P(A ∩ B) = P(B) = q = 0.5, which is not zero. Therefore, A and B cannot be mutually exclusive in this case. This option violates mutual exclusivity because the nonzero probability of B implies a nonzero probability of A ∩ B.

Option 3: p=0.5 and q=0.5
- With P(A) = 0.5 and P(B) = 0.5, there is a possibility that A and B occur together, depending on how A and B relate to each other. If A and B are not guaranteed to be disjoint, the intersection could have a positive probability, so mutual exclusivity is not guaranteed. Without additional information restricting their overlap, this option does not ensure P(A ∩ B) = 0. Hence this option is not generally correct.

Summary of reasoning: The only option among the provided choices that guarantees mutual exclusivity under the usual interpretation (that P(A ∩ B) = 0) is p=0 and q=0, since neither event can occur. The other listed combinations imply a nonzero chance of at least one of the events occurring, which can lead to a nonzero intersection in at least some models, contradicting mutual exclusivity.

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Final Exam - TUE Dec 09 2025 - Requires Respondus LockDown Browser

Under which values of p and q, are the events A and B mutually exclusive? (Check all that apply.)

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