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Mutually Exclusive
Definition: Mutually exclusive events are two or more events that cannot occur at the same time. In other words, the occurrence of one event means the other cannot happen. This concept is often used in probability theory and statistics.
Key Aspects:
1. Probability Context:
o Formula: If events A and B are mutually exclusive, P(A∩B)=0P(A \cap B) = 0P(A∩B)=0. The probability of both events happening simultaneously is zero.
o Example: When flipping a coin, the events "landing on heads" and "landing on tails" are mutually exclusive.
2. Statistical Analysis:
o Non-overlapping Sets: In a Venn diagram, mutually exclusive events are represented by non-overlapping circles.
o Calculation: The probability of either event A or event B occurring is the sum of their individual probabilities: P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)P(A∪B)=P(A)+P(B).
3. Decision Making:
o Resource Allocation: When choosing between mutually exclusive projects, only one can be selected, requiring careful consideration of costs and benefits.
o Strategic Choices: In business strategy, mutually exclusive options might involve choosing one market entry mode over another.

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