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Mutually Exclusive Events And Independent Events

Faizan Mohammad
24 Jun 0 0

Mutually Exclusive Events and Independent Events:

"Two events are said to be Mutually exclusive even "ts with respect to each other if occurrence of one excludes the occurrence of the other "

  • For example : If two men, say M1 and M2  proposed the same lady W for marriage and A and B are two events defined as follows : A =" M1gets married to  W" and B="M2 gets married to W"
  • Now from the example mentioned above it is quite clear that the events  A and B can not happen at the same time,i.e., occurrence of event A excludes the occurrence of event B and vice versa so we can say that the events A and B are two mutually exclusive events.
  • On the other hand two events are said to be Independent Events if occurrence of one event does not affect the occurrence of the other.
  • For example if a man M1 proposed to a woman W1 and a man M2 proposed to another woman W2. Now in this case if A and B are events such that A = "M1 gets married to W1" and B ="M2 gets married to W2", clearly the events A and B do not affect each other in any way. Thus here in this case the events A and B are Independent Events. 
  • Addition Theorem of Probabilities: If A and B are two mutually exclusiveevents, then Probability ( A ? B) = Probability (A) + Probability (B) 
  • It may also be written as P(A ? B) =P(A) +P(B) or P(A or B) = P(A) + P(B) 

Multiplication Theorem of Probabities:

"If A and B are two independent events, then P(A ∩ B) = P(A).P(B)

 or P(A and B) = P(A) . P(B) "

 

 

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