Dear student We have,PA∪B=56PA∩B=561-PA∩B=56PA∩B=1-56=16Also PB=1-PB=1-23=13Clearly PA∩B=PAPB16=12×1316=16So, A and B are independent events Regards

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No links please 12. If , and - , are the events A and B independent ?

Dear student

We have, P (A \cup B) = \frac{5}{6} P (A \cap B) = \frac{5}{6} 1 - P (A \cap B) = \frac{5}{6} P (A \cap B) = 1 - \frac{5}{6} = \frac{1}{6} Also P (B) = 1 - P (B) = 1 - \frac{2}{3} = \frac{1}{3} Clearly P (A \cap B) = P (A) P (B) \frac{1}{6} = \frac{1}{2} \times \frac{1}{3} \frac{1}{6} = \frac{1}{6} So, A and B are independent events .

Regards