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  • Check whether the following probabilities P(A) and P(B) are consistently defined (ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8

12.(ii)     Check whether the following probabilities  P(A)  and  P(B)  are consistently defined  

 (ii)   P(A)=0.5,P(B)=0.4,P(A\cup B)=0.8

Answers (1)

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(ii)   Given, P(A)=0.5,P(B)=0.4,P(A\cup B)=0.8

We know,

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

\implies 0.8 = 0.5 + 0.4 - P(A \cap B)

\implies P(A \cap B) = 0.9 - 0.8 = 0.1

Therefore, P(A \cap B) < P(A) and P(A \cap B) < P(B) , which satisfies the condition.

Hence, the probabilities are consistently defined

Posted by

HARSH KANKARIA

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