Question

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 

 

Answer 1

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

Answer 2

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