what is condition for p(AorB)=P(A)+P(B) where P(X) =probability of x

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$$\begin{gathered} \mathrm{We} \mathrm{know} \mathrm{that} \\ \mathrm{P}\left(\mathrm{A}\cup \mathrm{B}\right)=\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)-\mathrm{P}\left(\mathrm{A}\cap \mathrm{C}\right) \\ \mathrm{Hence} \\ \mathrm{P}\left(\mathrm{A}\cup \mathrm{B}\right)=\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right) \mathrm{when} \\ \mathrm{P}\left(\mathrm{A}\cap \mathrm{C}\right)=0 \\ \mathrm{And} \mathrm{P}\left(\mathrm{A}\cap \mathrm{C}\right) \mathrm{is} 0 \mathrm{for} \mathrm{mutually} \mathrm{exclusive} \mathrm{events} \mathrm{i}.\mathrm{e}. \mathrm{when} \mathrm{occurrence} \mathrm{of} \\ \mathrm{one} \mathrm{of} \mathrm{event} \mathrm{rejects} \mathrm{the} \mathrm{possibility} \mathrm{of} \mathrm{occurrence} \mathrm{of} \mathrm{the} \mathrm{other} \mathrm{i}.\mathrm{e}. \mathrm{both} \\ \mathrm{events} \mathrm{cannot} \mathrm{occur} \mathrm{simultaneously}. \end{gathered}$$

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