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Q. What are Inclusive Events?
Ans.
Events that can occur at the same time are called inclusive events. For example, a student can belong to more than one club at one time. Events A and B are inclusive if their intersection is not empty, . Here is a Venn diagram showing inclusive events A and B:
Property: If A and B are inclusive, then P(A or B) = P(A) + P(B) or P(A and B). In words, this means that the probability of A OR B occurring is equal to the probability of A occurring plus the probability of B occurring. This property can be written .
Proof: Using the definition for probability, we have:
Since A and B are inclusive, we mustn't count the elements in both sets more than once.
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The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:
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