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1. Let A and B two events such that ( ) 1 31 7 

P A B , P(A B) and P(B) 

∩ = ∪ = = then 

6 45 10 

(A) A and B are independent (B) A and B are mutually exclusive (C)A 1 

 

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Ans : (A)
Hint : \(P(\bar{B})=\frac{7}{10} \Rightarrow P(B)=\frac{3}{10}\) \(P(A \cup B)=P(A)+P(B)-P(A \cap B) \Rightarrow P(A)=\frac{5}{9}\)
\(\therefore \mathrm{P}(\mathrm{A}) \times \mathrm{P}(\mathrm{B})=\frac{5}{9} \times \frac{3}{10}=\frac{1}{6}=\mathrm{P}(\mathrm{A} \cap \mathrm{B})\) \(\Rightarrow \mathrm{A}, \mathrm{B}\) are independent
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