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Question 10 Which of the following is not true for mutually exclusive events? A. Pr(A uu B)=Pr(A)+Pr(B) B. Pr(A nn B)=0 C. Pr(A uu B)^(')=1-Pr(A uu B) D. Pr(A nn B)=Pr(A)× Pr(B) E. Pr(A uu B)=Pr(A)+Pr(B)-Pr(A nn B)

Question 1010\newlineWhich of the following is not true for mutually exclusive events?\newlineA. Pr⁡(A∪B)=Pr⁡(A)+Pr⁡(B) \operatorname{Pr}(A \cup B)=\operatorname{Pr}(A)+\operatorname{Pr}(B) \newlineB. Pr⁡(A∩B)=0 \operatorname{Pr}(A \cap B)=0 \newlineC. Pr⁡(A∪B)′=1−Pr⁡(A∪B) \operatorname{Pr}(A \cup B)^{\prime}=1-\operatorname{Pr}(A \cup B) \newlineD. Pr⁡(A∩B)=Pr⁡(A)×Pr⁡(B) \operatorname{Pr}(A \cap B)=\operatorname{Pr}(A) \times \operatorname{Pr}(B) \newlineE. Pr⁡(A∪B)=Pr⁡(A)+Pr⁡(B)−Pr⁡(A∩B) \operatorname{Pr}(A \cup B)=\operatorname{Pr}(A)+\operatorname{Pr}(B)-\operatorname{Pr}(A \cap B)

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Q. Question 1010\newlineWhich of the following is not true for mutually exclusive events?\newlineA. Pr⁡(A∪B)=Pr⁡(A)+Pr⁡(B) \operatorname{Pr}(A \cup B)=\operatorname{Pr}(A)+\operatorname{Pr}(B) \newlineB. Pr⁡(A∩B)=0 \operatorname{Pr}(A \cap B)=0 \newlineC. Pr⁡(A∪B)′=1−Pr⁡(A∪B) \operatorname{Pr}(A \cup B)^{\prime}=1-\operatorname{Pr}(A \cup B) \newlineD. Pr⁡(A∩B)=Pr⁡(A)×Pr⁡(B) \operatorname{Pr}(A \cap B)=\operatorname{Pr}(A) \times \operatorname{Pr}(B) \newlineE. Pr⁡(A∪B)=Pr⁡(A)+Pr⁡(B)−Pr⁡(A∩B) \operatorname{Pr}(A \cup B)=\operatorname{Pr}(A)+\operatorname{Pr}(B)-\operatorname{Pr}(A \cap B)
  1. Question Prompt: Question prompt: Identify which statement is not true for mutually exclusive events.
  2. Definition of Mutually Exclusive Events: Mutually exclusive events cannot happen at the same time, so Pr(A∩B)\text{Pr}(A \cap B) must be 00.
  3. Calculation of Pr(A∪B)Pr(A \cup B): For mutually exclusive events, Pr(A∪B)Pr(A \cup B) is indeed Pr(A)+Pr(B)Pr(A) + Pr(B) because they cannot occur together.
  4. Complement of Pr(A∪B)Pr(A \cup B): The complement of Pr(A∪B)Pr(A \cup B) is 1−Pr(A∪B)1 - Pr(A \cup B), so option C is a true statement.
  5. Calculation of Pr(A ∩\cap B): For mutually exclusive events, Pr(A ∩\cap B) cannot be Pr(A) ×\times Pr(B) because Pr(A ∩\cap B) is 00, not the product of their individual probabilities.
  6. General Addition Rule: Option E is a general addition rule for any two events, not just for mutually exclusive events. For mutually exclusive events, Pr(A∩B)Pr(A \cap B) is 00, so Pr(A∪B)=Pr(A)+Pr(B)−0Pr(A \cup B) = Pr(A) + Pr(B) - 0, which simplifies to Pr(A)+Pr(B)Pr(A) + Pr(B).

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