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  •  If A and B are two events such that.   <img alt="P\left ( A\cup B \right )=P\left ( A\cap B \right )" src="https://learn.careers360.com/latex-image/?%5Cdpi%7B100%7D%20P%5Cleft%20%28

 If A and B are two events such that.   P\left ( A\cup B \right )=P\left ( A\cap B \right ) then the incorrect statement amongst the following statements is :

 

 

Option: 1

 A and B are equally likely


Option: 2

P\left ( A\cap B' \right )=0


Option: 3

P\left ( A'\cap B \right )=0


Option: 4

P\left ( A \right )+P\left ( B \right )= 1


Answers (1)

best_answer

As learnt in concept

Addition Theorem of Probability -

P\left ( A\cup B \right )= P\left ( A \right )+P\left ( B \right )-P\left ( A\cap B \right )

in general:

P\left ( A_{1}\cup A_{2}\cup A_{3}\cdots A_{n} \right )=\sum_{i=1 }^{n}P\left ( A_{i} \right )-\sum_{i< j}^{n}P\left ( A_{i}\cap A_{j} \right )+\sum_{i< j< k}^{n} P\left ( A_{i}\cap A_{j}\cap A_{k} \right )-\cdots -\left ( -1 \right )^{n-1}P\left ( A_{1}\cap A_{2}\cap A_{3}\cdots \cap A_{n} \right )

-

 

P\left ( A\cup B \right )= P\left ( A\cap B \right )

P(A\cup B )= P(A)+P(B)-P(A\cap B )

P(A)+P(B)=P\left ( A\cup B \right )+P\left ( A\cap B \right )

(1), (2), (3) can be  true

But P(A) + P(B) can't be equal to 1

Posted by

Ritika Kankaria

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